#### Answer

$x=3$ or $x=1$

#### Work Step by Step

Subtract 1 on both sides of the equation to obtain:
$x-1=\sqrt{2x-2}$
Square both sides of the equation to obtain:
$(x-1)^2=2x-2$
Use the rule $(a-b)^2 = a^2 - 2ab+b^2$ where $a=x$ and $b=1$ to obtain:
$\\x^2-2x+1=2x-2$
Move all terms to the left side of the equation. Note that when a term is moved to the other side of the equation, its sign changes to its opposite.
$x^2-2x+1-2x+2=0
\\x^2-4x+3=0$
Factor the trinomial to obtain:
$(x-3)(x-1)=0$
Equate each factor to zero then solve each equation to obtain:
$x -3 = 0 \text{ or } x - 1 = 0
\\x = 3 \text{ or } x = 1$