Answer
$m= 2 $
Work Step by Step
Given\begin{equation}
\sqrt{-m+2}=m-2
\end{equation} First square both sides of the radical equation to eliminate the radical sign. Rearrange and solve for $w$.
\begin{equation}
\begin{aligned}
\left( \sqrt{-m+2}\right)^2&= \left( m-2\right)^2\\
-m+2& =m^2-4m+4\\
0& =m^2-3m+2\\
0 & = (m-2)(m-1)\\
\implies m& =1\\
m&= 2.
\end{aligned}
\end{equation} Check. \begin{equation}
\begin{aligned}
\sqrt{-1+2}& \stackrel{?}{=} 1-2 \\
1& =-1\quad \textbf{False}\\
\sqrt{-2+2}& \stackrel{?}{=} 2-2\\
0& =0\quad \checkmark.
\end{aligned}
\end{equation} The solution is $m= 2 $.
