Question 27815
Solve by completing the square:
{{{x^2 = 5x + 2}}} First, subtract 5x from both sides of the equation.
{{{x^2 - 5x = 2}}} Complete the square in the x-terms by adding the square of half the x-coefficient (that's {{{(5/2)^2 = (25/4)}}} to both sides of the equation.
{{{x^2 - 5x + 25/4 = 2 + 25/4}}}Simplify.
{{{(x - 5/2)^2 = 33/4}}} Now take the square root of both sides.
{{{x - 5/2 = (sqrt(33))/2}}} ...and , of course, the right side has a + or - in front.  Now add 5/2 to both sides.
{{{x = 5/2}}}+or-{{{(sqrt(33))/2}}}