Answer
$x= 522 $
Work Step by Step
Given \begin{equation}
\sqrt[5]{-2 x+20}=-4.
\end{equation} Start by rewriting the radical as a power of fraction and then solve for $x$.
\begin{equation}
\begin{aligned}
\sqrt[5]{-2 x+20}&=-4\\
\left(-2 x+20\right)^{\frac{1}{5}}&= -4\\
\left(\left(-2 x+20\right)^{\frac{1}{5}}\right)^5& = \left( -4\right)^5 \\
-2 x+20& =-1024\\
x&= \frac{-1024-20}{-2}\\
& = 522.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\left(-2\cdot( 522)+20\right)^{\frac{1}{5}}&\stackrel{?}{=}-4\\
-4& =-4\quad \checkmark
\end{aligned}
\end{equation} The solution is $x= 522$.
