# How do you solve this equation by factoring? 112x^2- 252= 0

marilynn07 | Certified Educator

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### 112x^2- 252= 0

Reorder the terms

-252+112x^2 = 0

Move all terms to the right of the equals sign that do not contain a variable

-252+112x^2 = 0

+252               +252

112x^2 = 252

divide each side by 112

112x^2/112 = 252/112

x^2 = 2.25

Now you can solve for x using the difference of 2 squares

(1.5+x)(-1.5+x) = 0

-1.5+x = 0   1.5+x = 0

x = 1.5      x = -1.5

(1.5, -1.5)

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givingiswinning | Student

112x^2- 252= 0

use the difference of 2 squares  (a – b)(a + b)

28 ( 2x - 3) ( 2x + 3)

set the parentheses equal to 0

2x - 3 =0

2x = 3

x = 3/2
2x + 3 = 0

2x = -3

x = -3/2
atyourservice | Student

112x^2- 252= 0

factor out the greatest common factor which is 28

`28 (4x^2 - 9 )`

use the difference of 2 squares  (a – b)(a + b)

28 ( 2x - 3) ( 2x + 3)

set the parentheses equal to 0

2x - 3 =0

2x = 3

x = 3/2  or 1.5

2x + 3 = 0

2x = -3

x = -3/2 or -1.5