Solve the equation by completing the square.
-$x ^ { 2 } + 12 x = - 26$
A) $- 12 + \sqrt { 26 }$
B) $6 + \sqrt { 10 }$
C) $- 6 - \sqrt { 10 } , - 6 + \sqrt { 10 }$
D) $6 - \sqrt { 26 } , 6 + \sqrt { 26 }$

Question

Quizplus · Accepted Answer

To solve the equation $x^2 + 12x = -26$ by completing the square, first move the constant term to the other side to get $x^2 + 12x + 26 = 0$. Then, add and subtract $(\frac{12}{2})^2 = 36$ inside the equation to complete the square: $x^2 + 12x + 36 = 36 + 26$. This simplifies to $(x + 6)^2 = 62$. Taking the square root of both sides gives $x + 6 = \pm \sqrt{62}$, which simplifies to $x = -6 \pm \sqrt{62}$. However, the correct simplification should be $x = -6 \pm \sqrt{36 + 26}$, which simplifies further to $x = -6 \pm \sqrt{62}$, indicating a mistake in my simplification process. Correctly, after adding the necessary term to complete the square, we should have $x^2 + 12x + 36 = 10$, leading to $(x + 6)^2 = 10$, and thus $x = -6 \pm \sqrt{10}$, which matches option C.

Solve the Equation by Completing the Square x2+12x=−26x ^ { 2 } + 12 x = - 26x2+12x=−26

Solve the Equation by Completing the Square $x ^ { 2 } + 12 x = - 26$