Answer
$\{3-\sqrt {22},3+\sqrt {22}\}$
Work Step by Step
Complete the square by adding $\left(\frac{6}{2}\right)^2=9$ to both sides.
$\Rightarrow x^2-6x+9=13+9$
Simplify.
$x^2-6x+9=22$
Factor on the left side.
$(x-3)^2=22$
Take the square root of both sides:
$\sqrt{(x-3)^2}=\pm \sqrt {22}$
$x-3=\pm \sqrt {22}$
Split the expression to obtain:
$x-3=\sqrt {22}$ or $x-3=-\sqrt {22}$
Add $3$ to both sides of both equations.
$x-3+3=\sqrt {22}+3\quad$ or $\quad x-3+3=-\sqrt {22}+3$
Simplify.
$x=3+\sqrt {22}\quad$ or $\quad x=3-\sqrt {22}$
Hence, the solution set is $\{3-\sqrt {22},3+\sqrt {22}\}$.
