Answer
$x=3.41$ and $x=0.59$
Work Step by Step
The given equation is
$\Rightarrow x^2-4x=-2$
Find the value of $(\frac{b}{2})^2$.
Substitute $-4$ for $b$.
$=(\frac{-4}{2})^2$
Simplify.
$=(-2)^2$
$=4$
Add $4$ to each side of the equation.
$\Rightarrow x^2-4x+4=-2+4$
Simplify.
$\Rightarrow x^2-4x+4=2$
Write the left side as the square of a binomial.
$\Rightarrow (x-2)^2=2$
Take the square root of each side.
$\Rightarrow x-2=\pm \sqrt{2}$
Add $2$ to each side.
$\Rightarrow x-2+2=\pm \sqrt{2} +2$
Simplify.
$\Rightarrow x=\pm \sqrt{2} +2$
The solutions are $x=\sqrt{2} +2=3.41$ and $x=-\sqrt{2} +2=0.59$.