Answer
$\color{blue}{\left\{3-\sqrt2, 3+\sqrt2\right\}}$
Work Step by Step
Add $7$ to both sides of the equation to obtain:
$x^2-6x+7=0$
RECALL:
The quadratic equation $ax^2+bx+c=0$ can be solved using the quadratic formula:
$x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$
The given equation has:
$a=1, b=-6, c=7$
Substitute these values into the quadratic formula to obtain:
$x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(7)}}{2(1)}
\\x=\dfrac{6\pm\sqrt{36-28}}{2}
\\x=\dfrac{6\pm\sqrt{8}}{2}
\\x=\dfrac{6\pm\sqrt{4(2)}}{2}
\\x=\dfrac{6\pm2\sqrt{2}}{2}
\\x=3 \pm \sqrt2$
Thus, the solution set is $\color{blue}{\left\{3-\sqrt2, 3+\sqrt2\right\}}$.
