Solve the equation by completing the square.
-$x ^ { 2 } + 18 x + 58 = 0$
A) $- 18 + \sqrt { 58 }$
B) $9 + \sqrt { 23 }$
C) $- 9 - \sqrt { 23 } , - 9 + \sqrt { 23 }$
D) $9 - \sqrt { 58 } , 9 + \sqrt { 58 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 18x + 58 = 0$ by completing the square, first move the constant term to the other side: $x^2 + 18x = -58$. Then, add $(\frac{18}{2})^2 = 81$ to both sides to complete the square: $x^2 + 18x + 81 = 81 - 58$. This simplifies to $(x + 9)^2 = 23$. Taking the square root of both sides gives $x + 9 = \pm\sqrt{23}$, leading to the solutions $x = -9 \pm \sqrt{23}$.

Solve the Equation by Completing the Square x2+18x+58=0x ^ { 2 } + 18 x + 58 = 0x2+18x+58=0

Solve the Equation by Completing the Square $x ^ { 2 } + 18 x + 58 = 0$