Answer
$x=2,3$
Work Step by Step
To complete the square, add a term that is the square of half the coefficient of $x$ to both sides of the equation, and factor the left side. Then use the square root property to simplify both sides, and then isolate $x$.
$x^2-5x+6=0$
$(\frac{-5}{2})^2$
$x^2-5x+6-6+(\frac{-5}{2})^2=-6+(\frac{-5}{2})^2$
$x^2-5x+(\frac{-5}{2})^2=-6+(\frac{-5}{2})^2$
$x^2-5x+\frac{25}{4}=-6+\frac{25}{4}$
$x^2-5x+\frac{25}{4}=\frac{1}{4}$
$(x-\frac{5}{2})^2=\frac{1}{4}$
$x-\frac{5}{2}=±\frac{1}{2}$
$x=\frac{5}{2}±\frac{1}{2}$
$x=2,3$
