Answer
$ x=3+5i,\quad x=3-5i$.
Work Step by Step
Given \begin{equation}
x^2-6 x+30=-4.
\end{equation} Rearrange and use the quadratic formula.
\begin{equation}
\begin{aligned}
x^2-6 x+30&=-4\\
x^2-6 x+34&=0\\
\end{aligned}
\end{equation} Find the solutions:
\begin{equation}
\begin{aligned}
x & =\frac{-(-6) \pm \sqrt{(-6)^2-4 \cdot 1 \cdot 34}}{2 \cdot 1}\\
& =\frac{6\pm \sqrt{-100}}{2} \\
&= \frac{6 \pm 10 i}{2 } \\
\therefore &x= 3+5i\\
x&= 3-5i.
\end{aligned}
\end{equation} The solution is $ x=3+5i,\quad x=3-5i$..
