Answer
$x=3-2\sqrt 5,3+2\sqrt 5$
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 $x$.
$x^2-6x-11=0$
$(\frac{-6}{2})^2=(-3)^2$
$x^2-6x-11+11+(-3)^2=11+(-3)^2$
$x^2-6x+(-3)^2=11+(-3)^2$
$x^2-6x+9=11+9$
$x^2-6x+9=20$
$(x-3)^2=20$
$x-3=±\sqrt {20}$
$x=3±2\sqrt 5$
$x=3-2\sqrt 5,3+2\sqrt 5$
