Answer
$\{3\pm\sqrt{2}\}$.
Work Step by Step
Subtract $7$ from both sides of the given equation.
$\Rightarrow x^2-6x+7-7=0-7$
$\Rightarrow x^2-6x=-7$
To complete the square on the left hand side we add the square of the half of the coefficient of the $x-$ term.
Add $(\frac{-6}{2})^2=3^2=9$ to both sides.
$\Rightarrow x^2-6x+9=-7+9$
Complete the square on the left hand side.
$\Rightarrow (x-3)^2=2$
Apply the Square Root Property.
$x-3=\sqrt{2}$ or $x-3=-\sqrt{2}$
Add $3$ to both sides.
$x-3+3=\sqrt{2}+3$ or $x-3+3=-\sqrt{2}+3$
Simplify.
$x=3+\sqrt{2}$ or $x=3-\sqrt{2}$
The solution set is $\{3+\sqrt{2},3-\sqrt{2}\}$
Or we can write
$=\{3\pm\sqrt{2}\}$.
