Answer
$x=8$ and $x=-2$.
Work Step by Step
The given equation is
$\Rightarrow x^2-6x=16$
Find the value of $(\frac{b}{2})^2$.
Substitute $-6$ for $b$.
$=(\frac{-6}{2})^2$
Simplify.
$=(-3)^2$
$=9$
Add $9$ to each side of the equation.
$\Rightarrow x^2-6x+9=16+9$
Simplify.
$\Rightarrow x^2-6x+9=25$
Write the left side as the square of a binomial.
$\Rightarrow (x-3)^2=25$
Take the square root of each side.
$\Rightarrow x-3=\pm 5$
Add $3$ to each side.
$\Rightarrow x-3+3=\pm 5+3$
Simplify.
$\Rightarrow x=\pm 5+3$
The solutions are $x=5+3=8$ and $x=-5+3=-2$.
