Answer
$\{9\} $
Work Step by Step
Start by squaring both sides of the equation to get rid of the radical sign. Expand the right side carefully as shown.
\begin{equation}
\begin{aligned}
\left(\sqrt{x-8}\right)^2& =\left(\sqrt{x}-2 \right)^2\\
x-8& = \left(\sqrt{x}-2 \right)\left(\sqrt{x}-2 \right)\\
x-8& =\left(\sqrt{x}-2 \right)\sqrt{x}-2\left(\sqrt{x}-2 \right)\\
x-8& =\left(\sqrt{x} \right)^2-2\sqrt{x}-2\sqrt{x}+2^2\\
x-8& =x-4\sqrt{x}+4\\
x-x-8-4&=-4\sqrt{x}\\
-12& = -4\sqrt{x}\\
\frac{-12}{-4}&= \sqrt{x}\\
3^2&=\left(\sqrt{x}\right)^2\\
9&= x
\end{aligned}
\end{equation}
The solution set is: $\{9\} $.
