Question 66792
Solve by completing the square:
{{{2x^2-12x-18 = 0}}} First, you want to get the coefficient of the {{{x^2}}} term to be 1, so divide everything by 2.
{{{(2x^2-12x-18)/2 = 0/2}}} Simplify.
{{{x^2-6x-9 = 0}}} Now move the constant term (-9) to the right side of the equation by adding 9 to both sides.
{{{x^2-6x = 9}}} Next, add the square of half the x-coefficient {{{((-6)/2)^2 = (-3)^2}}} = 9 to both sides.
{{{x^2-6x+9 = 18}}} Now factor the left side.
{{{(x-3)^2 = 18}}} Take the square root of both sides.
{{{x-3 }}} = +/-{{{sqrt(18)}}} Add 3 to both sides.
{{{x = 3+-sqrt(18)}}} Simplify. Note that: {{{sqrt(18) = sqrt(9*2)}}} = {{{3sqrt(2)}}}
{{{x1 = 3+3sqrt(2)}}}
{{{x2 = 3-3sqrt(2)}}}