Question 15667
Solve for x by completing the square.

{{{x^2 + 3x = -1}}}  Complete the square in the x-terms by adding the square of half the coefficient of x to both sides. This means adding {{{((1/2)3)^2 = 9/4}}}.

{{{x^2 + 3x + 9/4 = -1 + 9/4}}} Factor the left side.
{{{(x + 3/2)^2 = 5/4}}}  Take the square root of both sides.
{{{x + 3/2 = sqrt(5/4)}}} Subtract 3/2 from both sides.
{{{x = -3/2 + sqrt(5)/2}}} or {{{x = -3/2 - sqrt(5)/2}}}
{{{x = (-3+sqrt(5))/2}}} or {{{x = (-3-sqrt(5))/2}}}