Question 15483
Solve by completing the square:

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

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