Question

If (x + 5)(x - 2) = 18, then which of the following statements is true?

A.) x + 7 = 0 or x - 4 = 0
B.) x + 5 = 0 or x - 2 = 0
C.) x + 5 = 6 or x - 2 = 3

Answer 1

Collect like terms first before you Slove

Answer 2

The correct answer is option A.

Explanation:

(x + 5)(x - 2) = 18

Using identity :

`(x+a)(x+b)=x^2+(a+b)x+ab`

x = x, a = 5, b = -2

`(x + 5)(x - 2) = 18`

`x^2+(5+(-2))x+5* (-2)=18`

`x^2+3x-10=18`

`x^2+3x-28=0`

Using Middle term splitting method to factorize:

`x^2+7x-4x-28=0`

`x(x+7)+(-4)(x+7)=0`

`(x+7)(x-4)=0`

So, we have two solutions of x:

1)
`(x+7)=0`

2)
`(x-4)=0`