Solve the equation by completing the square. Express any complex numbers using i notation.
-$x^{2}+12 x=-23$
A)$ x=-12 + \sqrt{13} $
B) $ x=-6 \pm \sqrt{13} $
C) $ x=6+\sqrt{13} $
D) $ x=6 \pm \sqrt{23} $

Question

Quizplus · Accepted Answer

To solve the equation $x^{2} + 12x = -23$ by completing the square, first move all terms to one side to set the equation to zero: $x^{2} + 12x + 23 = 0$. Then, add and subtract $(\frac{12}{2})^2 = 36$ inside the equation to complete the square: $x^{2} + 12x + 36 = 36 - 23$. This simplifies to $(x + 6)^2 = 13$, leading to $x + 6 = \pm \sqrt{13}$, and finally, $x = -6 \pm \sqrt{13}$.

Solve the Equation by Completing the Square x2+12x=−23x^{2}+12 x=-23x2+12x=−23 A) x=−12+13 x=-12 + \sqrt{13} x=−12+13​

Solve the Equation by Completing the Square $x^{2}+12 x=-23$ A) $x=-12 + \sqrt{13}$