Answer
$x= 32$
Work Step by Step
Given \begin{equation}
5 \sqrt{2 x}=40.
\end{equation} Start by squaring both sides of the equation to eliminate the radical sign and solve for $x$. \begin{equation}
\begin{aligned}
5 \sqrt{2 x}& = 40 \\
\left( 5 \sqrt{2 x} \right)^2&= \left( 40 \right)^2\\
25\cdot 2 x& = 1600\\
x& =\frac{1600}{50}\\
&= 32.
\end{aligned}
\end{equation} Check.
\begin{equation} \begin{aligned}
5 \sqrt{2 \cdot 32} & \stackrel{?}{=} 40 \\
40& =40
\end{aligned}
\end{equation} The solution is $x= 32$.
