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

Explanation:

Step1: Rearrange the equation

Subtract 36 from both sides: $x^2 + 20x + 100 - 36 = 0$ $x^2 + 20x + 64 = 0$

Step2: Factor the quadratic

Find two numbers that multiply to 64 and add to 20 (16 and 4): $(x + 16)(x + 4) = 0$

Step3: Solve for x

Set each factor equal to 0: $x + 16 = 0 \implies x = -16$ $x + 4 = 0 \implies x = -4$

Answer:

x = -16 or x = -4