Answer
$x=10$
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(
\sqrt{2x-4}
\right)^2=\left(
x-6
\right)^2
\\\\
2x-4=(x)^2+2(x)(-6)+(-6)^2
\\\\
2x-4=x^2-12x+36
\\\\
0=x^2+(-12x-2x)+(36+4)
\\\\
x^2-14x+40=0
\\\\
(x-10)(x-4)=0
\\\\
x=\{4,10\}
.\end{array}
Upon checking, only $
x=10
$ satisfies the original equation.
