SOLUTION: Use the quadratic formula to solve the equation. {{{x^2-x=-1}}}

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Question 282591: Use the quadratic formula to solve the equation.
x%5E2-x=-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-x=-1 Start with the given equation.


x%5E2-x%2B1=0 Add 1 to both sides.


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


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


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


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


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


x+=+%281+%2B-+sqrt%28+-3+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%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+=+%281%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%281-i%2Asqrt%283%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%281%2Bi%2Asqrt%283%29%29%2F%282%29 or x+=+%281-i%2Asqrt%283%29%29%2F%282%29