Question

solve for x. write both solutions, separated by a comma. 2x² + 9x + 9 = 0 enter the correct answer.

Explanation:

Step1: Factor the quadratic equation

Find two numbers that multiply to $2\times9=18$ and add to $9$ (these numbers are 6 and 3). Rewrite and factor:
$2x^2 + 6x + 3x + 9 = 0$
$2x(x+3) + 3(x+3) = 0$
$(2x+3)(x+3) = 0$

Step2: Set each factor to 0 and solve

First factor:
$2x+3=0$
$2x=-3$
$x=\frac{-3}{2}$

Second factor:
$x+3=0$
$x=-3$

Answer:

$-3, -\frac{3}{2}$