Question

solve for x:

1. $2x^{2}+6x - 36 = 0$

Explanation:

Step1: Simplify the equation

Divide all terms by 2:
$\frac{2x^2}{2} + \frac{6x}{2} - \frac{36}{2} = \frac{0}{2}$
$x^2 + 3x - 18 = 0$

Step2: Factor the quadratic

Find two numbers that multiply to -18 and add to 3 (6 and -3):
$(x + 6)(x - 3) = 0$

Step3: Solve for x

Set each factor equal to 0:
$x + 6 = 0$ or $x - 3 = 0$

Answer:

$x = -6$ or $x = 3$