Answer
$1+\sqrt6$ or $1-\sqrt6$
Work Step by Step
The coefficient of x is -2.
Adding the square of half the coefficient of x creates a perfect square.
$(-2\div2)^2=(-1)^2=1$
$x^2-2x=5$
Add the square of half the coefficient of x to each side of the equation.
$x^2-2x+1=5+1$
Simplify.
$x^2-2x+1=6$
Factor the polynomial.
$(x-1)^2=6$
Take the square root of each side.
$\sqrt{(x-1)^2}=\sqrt 6$
Simplify.
$x-1=\pm \sqrt 6$
Add 1 to each side.
$x-1+1=\pm \sqrt 6+1$
Simplify.
$x=1+\sqrt6$ or $x=1-\sqrt6$
