Answer
$x= -1555 $
Work Step by Step
Given \begin{equation}
\sqrt[5]{2 x-15}+9=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-15}+9&=4\\
\left(5 x+2\right)^{\frac{1}{5}}&= 4\\
\left(\left(2 x-15\right)^{\frac{1}{5}}\right)^3& = \left( -5\right)^5 \\
2 x-15& =-3125\\
x&= \frac{-3125+15}{2}\\
& = -1555.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\left(2 \cdot(-1555)-15\right)^{\frac{1}{5}}+9&\stackrel{?}{=}4\\
4& =4\quad \checkmark.
\end{aligned}
\end{equation} The solution is $x= -1555 $.
