Solve the equation by using the square root property or completing the square.
-$4 x^{2}+16 x=64$
A) $\{-2+2 \sqrt{5},-2-2 \sqrt{5}\}$
B) $\{2+2 \sqrt{10}, 2-2 \sqrt{10}\}$
C) $\{2+2 \sqrt{5}, 2-2 \sqrt{5}\}$
D) $\{-4+2 \sqrt{10},-4-2 \sqrt{10}\}$

Question

Quizplus · Accepted Answer

First, subtract 64 from both sides to set the equation to zero: $4x^2 + 16x - 64 = 0$. Then, divide the entire equation by 4 to simplify: $x^2 + 4x - 16 = 0$. Completing the square, we add 16 to both sides to balance the equation after adding $(4/2)^2 = 4$, resulting in $x^2 + 4x + 4 = 20$. Taking the square root of both sides gives $x + 2 = \pm \sqrt{20}$, which simplifies to $x = -2 \pm 2\sqrt{5}$.

Solve the Equation by Using the Square Root Property or Completing