Use the zero product property to find the solutions to the equation (x + 2) (x + 3) = 12.

Question

asked Feb 18, 2020 122k views

2 Answers

Kmkemp · Answer 1 · 2020-02-24T21:00:07+0000

Answer:

$x_(1) =-6\\x_(2) =1$

Explanation:

The given equation is

(x+2)(x+3)=12

First, we need to apply distributive property to have the quadratic expression

$x^(2) +3x+2x+6=12\\x^(2) +5x+6-12=0\\x^(2) +5x-6=0$

We need to find two numbers which product is -6 and which difference is 5. Those numbers are 6 and 1, because 6 - 1 = 5, and 6(-1) = -6.

x^(2) +5x-6=(x+6)(x-1)=0

If we apply the zero product property, that means each binomial is equal to zero

$x+6=0\\x-1=0$

Therefore, the solutions are

$x_(1) =-6\\x_(2) =1$