Answer
$x=9$
Work Step by Step
Squaring both sides of the equation and then using the properties of equality, we obtain:
\begin{array}{l}\require{cancel}\left(
2\sqrt{x}
\right)^2=\left(
x-3
\right)^2
\\\\
4x=(x)^2+2(x)(-3)+(-3)^2
\\\\
4x=x^2-6x+9
\\\\
0=x^2+(-6x-4x)+9
\\\\
x^2-10x+9=0
\\\\
(x-9)(x-1)=0
\\\\
x=\{1,9\}
.\end{array}
Upon checking, only $
x=9
$ satisfies the original equation.
