Answer
$7-\sqrt{3}\ i$; $7+\sqrt{3}\ i$
Work Step by Step
Given \begin{equation}
2(a-7)^2+11=5.
\end{equation} This equation can be best solved by using the square root property.
\begin{equation}
\begin{aligned}
2(a-7)^2+11&=5\\
(a-7)^2&=\frac{5-11}{2}\\
(a-7)^2&= -3\\
a-7&= \pm \sqrt{-3}\\
a&=7\pm \sqrt{3}\ i.
\end{aligned}
\end{equation} The solution is \begin{equation}
a= 7-\sqrt{3}\ i\ ,\quad a= 7+\sqrt{3}\ i.
\end{equation}
