Answer
$x=\{ 2,3 \}$
Work Step by Step
Isolating the radical expression on one side and then squaring both sides, the solution/s of the given equation, $
x=\sqrt{x-2}+2
,$ is/are
\begin{array}{l}\require{cancel}
x-2=\sqrt{x-2}
\\\\
(x-2)^2=(\sqrt{x-2})^2
\\\\
(x)^2+2(x)(-2)+(-2)^2=x-2
\\\\
x^2-4x+4=x-2
\\\\
x^2+(-4x-x)+(4+2)=0
\\\\
x^2-5x+6=0
\\\\
(x-3)(x-2)=0
\\\\
x=\{ 2,3 \}
.\end{array}
Upon checking, both solutions satisfy the original equation. Hence, $
x=\{ 2,3 \}
.$
