Answer
$x = 8- 2\sqrt{\frac{2}{3}}\ i$
$x = 8+ 2\sqrt{\frac{2}{3}}\ i$
Work Step by Step
Given the quadratic equation
\begin{equation}
3(x-8)^2+12=4.
\end{equation} This equation can be best solved by completing the square. \begin{equation}
\begin{aligned}
3(x-8)^2+12&=4\\
(x-8)^2&=-8\\
(x-8)^2&=-\frac{8}{3}\\
x-8&=\pm\sqrt{-4\cdot\frac{2}{3}}\\
x&=8\pm\sqrt{-4\cdot\frac{2}{3}} \\
x& = 8\pm 2\sqrt{\frac{2}{3}}\ i.
\end{aligned}
\end{equation}The solution is \begin{equation}
\begin{aligned}
x & = 8- 2\sqrt{\frac{2}{3}}\ i \\
x & = 8+ 2\sqrt{\frac{2}{3}}\ i.
\end{aligned}
\end{equation}
