Solve the equation by completing the square.
-$x ^ { 2 } + 41 = - 16 x$
A) $8 + \sqrt { 23 }$
B) $- 8 - \sqrt { 23 } , - 8 + \sqrt { 23 }$
C) $8 - \sqrt { 41 } , 8 + \sqrt { 41 }$
D) $- 16 + \sqrt { 41 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 41 = -16x$ by completing the square, first move all terms to one side to get $x^2 + 16x + 41 = 0$. Then, to complete the square, add and subtract $(\frac{16}{2})^2 = 64$ inside the equation, leading to $x^2 + 16x + 64 = 64 - 41$. This simplifies to $(x + 8)^2 = 23$, and taking the square root of both sides gives $x + 8 = \pm \sqrt{23}$. Solving for $x$ yields $x = -8 \pm \sqrt{23}$, which matches choice B.

Solve the Equation by Completing the Square x2+41=−16xx ^ { 2 } + 41 = - 16 xx2+41=−16x

Solve the Equation by Completing the Square $x ^ { 2 } + 41 = - 16 x$