Solve the equation by completing the square. $4 x ^ { 2 } = 20 - 32 x$
A) $x = 32$ , $x = - \sqrt { 6 }$
B) $x = - 4 \pm \sqrt { 21 }$
C) $x = 6 \pm \sqrt { 6 }$
D) $x = 4 \pm \sqrt { 21 }$
E) $x = 4$ , $x = - 4$

Question

Quizplus · Accepted Answer

To solve the equation $4x^2 = 20 - 32x$ by completing the square, first move all terms to one side to get $4x^2 + 32x - 20 = 0$. Divide the entire equation by 4 to simplify: $x^2 + 8x - 5 = 0$. To complete the square, add and subtract $(\frac{8}{2})^2 = 16$ inside the equation, leading to $x^2 + 8x + 16 - 16 - 5 = 0$, which simplifies to $(x + 4)^2 = 21$. Taking the square root of both sides gives $x + 4 = \pm \sqrt{21}$, so $x = -4 \pm \sqrt{21}$.

Solve the Equation by Completing the Square 4x2=20−32x4 x ^ { 2 } = 20 - 32 x4x2=20−32x

Solve the Equation by Completing the Square $4 x ^ { 2 } = 20 - 32 x$