Answer
$x=2$
Work Step by Step
Using the properties of equality, the given equation, $
\sqrt{8x}-2=x
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{8x}=x+2
.\end{array}
Squaring both sides of the equation and then using the properties of equality, we obtain:
\begin{array}{l}\require{cancel}\left(
\sqrt{8x}
\right)^2=\left(
x+2
\right)^2
\\\\
8x=(x)^2+2(x)(2)+(2)^2
\\\\
8x=x^2+4x+4
\\\\
0=x^2+(4x-8x)+4
\\\\
x^2-4x+4=0
\\\\
(x-2)^2=0
\\\\
x=2
.\end{array}
Upon checking, $
x=2
$ satisfies the original equation.
