Answer
$x=\{ 0,3 \}$
Work Step by Step
By squaring both sides of the equal sign, the value of $x$ in $
\sqrt{4-x}=x-2
$ is
\begin{array}{l}
\left( \sqrt{4-x} \right)^2=(x-2)^2
\\\\
4-x=(x)^2+2(x)(-2)+(-2)^2
\\\\
4-x=x^2-4x+4
\\\\
-x^2+(-x+4x)+(4-4)=0
\\\\
-x^2+3x=0
\\\\
x^2-3x=0
\\\\
x(x-3)=0
\\\\
x=\{ 0,3 \}
.\end{array}
