QUADRATIC EQUATION

e.g. 1. Difference of Perfect Squares Technique

x² - 49 = 0

find square root

( x - 7 ) ( x + 7 ) = 0

find the value of x

x - 7 = 0 x + 7 = 0

x = 7 x = -7

final answer:

x = 7, x = -7

e.g. 2.

3x² - 75 = 0

find the GCF

GCF = 3

Divide the problem by the GCF

3 [ x² - 25 ]

Use the Difference of Perfect Squares Technique

3 ( x - 5 ) ( x + 5 )

find the value of x

x - 5 = 0 x + 5 = 0

x = 5 x = -5

final answer:

x = 5, x = -5

e.g. 3.

9x² - 64 = 0

use difference of perfect squares technique

( 3x - 8 ) ( 3x + 8 )

find the value of x

3x + 8 = 0 3x - 8 = 0

3x = -8 3x = 8

x = -8/3 x = 8/3

final answer:

x = -8/3, x = 8/3

e.g. 4.

8x² + 2x - 15 = 0

Multiply 8 and -15

8 x -15 = -120

find the multiples of -120 that equals to +2 when added.

-10 × 12 = -120

-10 + 12 = +2

replace +2x by 12x - 10x

8x² + 12x - 10x - 15 = 0

find the GCF from the FIRST two terms

GCF = 4x

now divide the problem by the GCF

4x ( 2x + 3 )

find the GCF from the LAST two terms

GCF = -5

divide the last two terms by the GCF

-5 ( 2x + 3 )

combine

4x ( 2x + 3 ) -5 ( 2x + 3 )

( 4x - 5 )( 2x + 3 ) = 0

fine the value of x

4x - 5 = 0 2x + 3 = 0

4x = 5 2x = - 3

x = 5/4 x = -3/2

final answer:

x = 5/4, x = -3/2