Answer
$-5+ i\frac{\sqrt{2}}{2}$; $-5- i\frac{\sqrt{2}}{2}$
Work Step by Step
Given \begin{equation}
-4(x+5)^2+7=9.
\end{equation} Use the square root property to solve for $x$.
\begin{equation}
\begin{aligned}
-4(x+5)^2+7&=9\\
(x+5)^2&= \frac{9-7}{-4}\\
(x+5)^2& = -\frac{1}{2}\\
x+5&=\pm \frac{\sqrt{-1}}{\sqrt{2}}\\
x+5&=\pm \frac{i}{\sqrt{2}}\cdot \frac{\sqrt{2}}{\sqrt{2}}\\
x& = -5\pm i\frac{\sqrt{2}}{2}.
\end{aligned}
\end{equation} The solution is $$ x= -5+ i\frac{\sqrt{2}}{2} \quad , x= -5- i\frac{\sqrt{2}}{2}.$$
