Answer
$x=5$ and $x=3$.
Work Step by Step
The given equation is
$\Rightarrow x^2-8x+15=0$
Find the value of $(\frac{b}{2})^2$.
Substitute $-8$ for $b$.
$=(\frac{-8}{2})^2$
Simplify.
$=(-4)^2$
$=16$
Add $1$ to each side of the equation.
$\Rightarrow x^2-8x+15+1=0+1$
Simplify.
$\Rightarrow x^2-8x+16=1$
Write the left side as the square of a binomial.
$\Rightarrow (x-4)^2=1$
Take the square root of each side.
$\Rightarrow x-4=\pm1$
Add $4$ from each side.
$\Rightarrow x-4+4=\pm1+4$
Simplify.
$\Rightarrow x=\pm1+4$
The solutions are $x=1+4=5$ and $x=-1+4=3$.
