SOLUTION: Please help me solve, step by step this equation: x^2+x+1=0

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Question 779018: Please help me solve, step by step this equation:
x^2+x+1=0
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+x+1 cannot be factored because it is not a square trinomial. Subtract 1 from both sides, and then decide what to add to x^2+x to make it a square factorable trinomial! Study the derivation of Completing the Square. The term to add is (1/2)^2=1/4.

Knowing THAT, let's start from the original equation again and use the term.

x%5E2%2Bx%2B1=0
x%5E2%2Bx+=-1
x%5E2%2Bx%2B1%2F4=-1%2B1%2F4
%28x%2B1%2F2%29%5E2=-1%2B1%2F4 which you should finish on your own.