Answer
$x=4$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{x}+2=x
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{x}=x-2
.\end{array}
Raising both sides to the second power, then the solution/s to the equation above is/are
\begin{array}{l}\require{cancel}
x=(x-2)^2
\\\\
x=(x)^2+2(x)(-2)+(-2)^2
\\\\
x=x^2-4x+4
\\\\
-x^2+(x+4x)-4=0
\\\\
-x^2+5x-4=0
\\\\
x^2-5x+4=0
\\\\
(x-4)(x-1)=0
\\\\
x=\left\{ 1,4 \right\}
.\end{array}
Upon checking, only $
x=4
$ satisfies the original equation.