Answer
$x= 1363.48$
Work Step by Step
Given \begin{equation}
-0.25 \sqrt{2.3 w}=-14.
\end{equation} Start by squaring both sides of the equation to eliminate the radical sign and solve for $w$. \begin{equation}
\begin{aligned}
-0.25 \sqrt{2.3 w}&=-14 \\
\left( -0.25 \sqrt{2.3 w} \right)^2&= \left( -14 \right)^2\\
0.0625\cdot 2.3 w& = 196\\
x& =\frac{196}{0.0625\cdot 2.3}\\
&\approx1363.478261.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
-0.25\sqrt{2.3 \cdot 1363.478261} & \stackrel{?}{=} -14 \\
-14& \approx-14\checkmark.
\end{aligned}
\end{equation} The solution is $x= 1363.48$.
