Answer
$x=3$ and $x=-1$
Work Step by Step
The given equation is
$\Rightarrow x^2-2x=3$
Find the value of $(\frac{b}{2})^2$.
Substitute $-2$ for $b$.
$=(\frac{-2}{2})^2$
Simplify.
$=(-1)^2$
$=1$
Add $1$ to each side of the euqation.
$\Rightarrow x^2-2x+1=3+1$
Simplify.
$\Rightarrow x^2-2x+1=4$
Write the left side as the square of a binomial.
$\Rightarrow (x-1)^2=4$
Take the square root of each side.
$\Rightarrow x-1=\pm2$
Add $1$ to each side.
$\Rightarrow x-1+1=1\pm2$
Simplify.
$\Rightarrow x=1\pm2$
The solutions are $x=1+2=3$ and $x=1-2=-1$.
