Answer
$x=1-\sqrt 6,1+\sqrt 6$
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 $x$.
$x^2-2x-5=0$
$(\frac{-2}{2})^2=(-1)^2$
$x^2-2x-5+5+(-1)^2=5+(-1)^2$
$x^2-2x+(-1)^2=5+(-1)^2$
$x^2-2x+1=5+1$
$x^2-2x+1=6$
$(x-1)^2=6$
$x-1=±\sqrt 6$
$x=1±\sqrt 6$
$x=1-\sqrt 6,1+\sqrt 6$
