Question

what is the solution to $2x^2 + 8x = x^2 - 16$?\
$x = 2$\
$x = 4$\
$x = -4$\
$x = -2$

Explanation:

Step1: Rearrange to standard form

Subtract $x^2 - 16$ from both sides:
$2x^2 + 8x - (x^2 - 16) = 0$
$x^2 + 8x + 16 = 0$

Step2: Factor the quadratic

Recognize perfect square trinomial:
$(x + 4)^2 = 0$

Step3: Solve for x

Set factor equal to 0:
$x + 4 = 0$
$x = -4$

Answer:

$x = -4$