SOLUTION: Solve x^2+x+1=0

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Question 354990: Solve x^2+x+1=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2%2Bx%2B1=0 Start with the given equation.


Notice that the quadratic x%5E2%2Bx%2B1 is in the form of Ax%5E2%2BBx%2BC where A=1, B=1, and C=1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=1


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%281%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%28-1+%2B-+sqrt%28+-3+%29%29%2F%282%281%29%29 Subtract 4 from 1 to get -3


x+=+%28-1+%2B-+sqrt%28+-3+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+i%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-1%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%28-1-i%2Asqrt%283%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%28-1%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%28-1-i%2Asqrt%283%29%29%2F%282%29