Question

solve for x in the equation $x^2 + 20x + 100 = 36$. $\bigcirc$ $x = -16$ or $x = -4$ $\bigcirc$ $x = -10$ $\bigcirc$ $x = -8$ $\bigcirc$ $x = 4$ or $x = 16$

Explanation:

Step1: Rewrite left side as square

$x^2 + 20x + 100 = (x+10)^2$
Equation becomes: $(x+10)^2 = 36$

Step2: Take square roots of both sides

$x+10 = \pm\sqrt{36}$
$x+10 = \pm6$

Step3: Solve for x (case 1)

$x+10 = 6$
$x = 6 - 10 = -4$

Step4: Solve for x (case 2)

$x+10 = -6$
$x = -6 - 10 = -16$

Answer:

$x=-16$ or $x=-4$