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Solving Equation= s
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Two expressions set eq= ual to each other is called
an equati= on. <= /div>
Solving Equation= s
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true. 
Solving Equation= s
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
We solve polynomial equations by factoring.
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
We solve polynomial equations by factoring.  = ;
To solve other algebra= ic equations, we have to transform them into polynomial equations.
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
Example A: 3x2 – 2x =3D 8
We solve polynomial equations by factoring.  = ;
To solve other algebra= ic equations, we have to transform them into polynomial equations.
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
Example A: 3x2 – 2x =3D 8
We solve polynomial equations by factoring.  = ;
To solve other algebra= ic equations, we have to transform them into polynomial equations.
Set one side to 0,  3x2 – 2x – 8 =3D 0  
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
Example A: 3x2 – 2x =3D 8
We solve polynomial equations by factoring.  = ;
To solve other algebra= ic equations, we have to transform them into polynomial equations.
Set one side to 0,  3x2 – 2x – 8 =3D 0    factor this;
(3x + 4)(x – 2) =3D 0 
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Two expressions set eq= ual to each other is called
an equati= on. To solve= an equation means to find vealue(s) for the vari= ables that makes the equation true.  Equations made from polynomial expressions, rational expressions, or algebraic expressions= are called polynomial equations, rational equations, or = algebraic equations respectively.
Solving Equation= s
Example A: 3x2 – 2x =3D 8
We solve polynomial equations by factoring.  = ;
To solve other algebra= ic equations, we have to transform them into polynomial equations.
Set one side to 0,  3x2 – 2x – 8 =3D 0    factor this;
(3x + 4)(x – 2) =3D 0  extract answers;
x =3D -4/3, 2
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Quadratic Formula and Discriminant
Quadratic Formula (QF):<= /div>
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Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
x =3D
–b ± Öb – 4ac
2a
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0130_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0130_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0131.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
x =3D
–b ± Öb – 4ac
2a
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0131_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0131_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots,
x =3D
–b ± Öb – 4ac
2a
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0132_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0132_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0132_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0133.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
x =3D
–b ± Öb – 4ac
2a
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0133_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0133_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0133_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0134.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
II. If b<= /span>2 – 4bc < 0, the roots are = not real.  
x =3D
–b ± Öb – 4ac
2a
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0134_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0134_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0134_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
II. If b<= /span>2 – 4bc < 0, the roots are = not real.  
x =3D
–b ± Öb – 4ac
2a
Example = B: Find the values k where the solutions are real= for x2 + 2x + (2 – 3k) =3D 0
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0135_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0135_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0135_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
II. If b<= /span>2 – 4bc < 0, the roots are = not real.  
x =3D
–b ± Öb – 4ac
2a
Example = B: Find the values k where the solutions are real= for x2 + 2x + (2 – 3k) =3D 0
We need b2 – 4ac > 0,
------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0136_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhjAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACL AAEAgAAAAAAAAAIKjI+py+0Po5z0FAA7 ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0136_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhUgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQBR AAEAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0136_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAO AAEAgAAAAAAAAAIDjI9YADt= ------=_NextPart_01C82E61.6014CB20 Content-Location: file:///C:/09764A33/3SolvingEquations_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
II. If b<= /span>2 – 4bc < 0, the roots are = not real.  
x =3D
–b ± Öb – 4ac
2a
Example = B: Find the values k where the solutions are real= for x2 + 2x + (2 – 3k) =3D 0
We need b2 – 4ac > 0, i.e  4 – 4(2 – 3k) > 0.=  
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Quadratic Formula and Discriminant
Quadra= tic Formula (QF):
The roots= for the equation ax2 + bx + c =3D 0 are
        = ;            
b<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>2 – 4ac is the discriminant because = its value indicates the type of roots we have.
I. If b2 – 4ac > 0, we have real r= oots, furthermore if
   b2 – 4ac is a perfect square, t= he roots are rational.
II. If b<= /span>2 – 4bc < 0, the roots are = not real.  
x =3D
–b ± Öb – 4ac
2a
Example = B: Find the values k where the solutions are real= for x2 + 2x + (2 – 3k) =3D 0
We need b2 – 4ac > 0, i.e  4 – 4(2 – 3k) > 0.=  
– 4 + 12k > 0
or        = ;  k > 1/3
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Equations= of the Form xp/q =3D c
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
Raise both sides to -3/2 power.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
Raise both sides to -3/2 power.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Raise both sides to -3/2 power.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
Raise both sides to 2/3 power.
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
Raise both sides to 2/3 power.
(2x – 3)=3D -8 &agrav= e;
[(2x – 3)]2/3 =3D (-8)2/3 
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
Raise both sides to 2/3 power.
(2x – 3)=3D -8 &agrav= e;
[(2x – 3)]2/3 =3D (-8)2/3 
(2x – 3) =3D 4
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
Raise both sides to 2/3 power.
(2x – 3)=3D -8 &agrav= e;
[(2x – 3)]2/3 =3D (-8)2/3 
(2x – 3) =3D 4
2x =3D 7 à x =3D 7/2
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Equations= of the Form xp/q =3D c
Solve xp/q =3D c by raising both sides to the reciprocal exponent q/p and check your answers afterwards.
Example C: Solve x=3D 16
x-2/3 =3D 16 <= /span>à
(x-2/3)= -3/2 =3D (16)= -3/2
x=3D 1/64  and it's a solution.
Example D: Solve (2x – 3)3/2 =3D -8
Raise both sides to -3/2 power.
Raise both sides to 2/3 power.
(2x – 3)=3D -8 &agrav= e;
[(2x – 3)]2/3 =3D (-8)2/3 
(2x – 3) =3D 4
2x =3D 7 à x =3D 7/2
Since x =3D 7/2 doesn't work because 43/2 = =3D -8.
There is no solution.
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Radical Equation= s
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= . 
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;      
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4     
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4       iso= late the radical;     
        = ;           8Öx  =3D  4x – 12        = ;     
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4       iso= late the radical;     
        = ;           8Öx  =3D  4x – 12        = ;       divide by 4;
        = ;            &n= bsp;             2Öx  =3D  x – 3        = ;        
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4       iso= late the radical;     
        = ;           8Öx  =3D  4x – 12        = ;       divide by 4;
        = ;            &n= bsp;             2Öx  =3D  x – 3        = ;         square again;
        = ;          ( 2Öx)2  =3D  (x – 3)
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4       iso= late the radical;     
        = ;           8Öx  =3D  4x – 12        = ;       divide by 4;
        = ;            &n= bsp;             2Öx  =3D  x – 3        = ;         square again;
        = ;          ( 2Öx)2  =3D  (x – 3)        = ;            &n= bsp;           4x =3D x– 6x + 9
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2 = ± 2AB + B2
Example E: Solve
     Öx + 4  =3D Ö5x + 4        = ;       square both sides;    
    (Öx + 4)2 =3D (Ö5x + 4 )2 
x + 2 * 4 Öx + 16  =3D 5x += 4       iso= late the radical;     
        = ;           8Öx  =3D  4x – 12        = ;       divide by 4;
        = ;            &n= bsp;             2Öx  =3D  x – 3        = ;         square again;
        = ;          ( 2Öx)2  =3D  (x – 3)        = ;            &n= bsp;           4x =3D x– 6x + 9
        = ;            &n= bsp;  0 =3D x– 10x + 9
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Radical Equation= s
Solve radical equation= s by squaring both sides to
remove the square root= .  Do it again if necessary.<= /div>
Reminder:&nbs= p; (A ± B)2 =3D A2