SOLUTION: Solve for x x^2-x+4=0

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Question 163020: Solve for x
x^2-x+4=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-x%2B4=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-1, and c=4


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%284%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-1, and c=4


x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%284%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-4%281%29%284%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


x+=+%281+%2B-+sqrt%28+1-16+%29%29%2F%282%281%29%29 Multiply 4%281%29%284%29 to get 16


x+=+%281+%2B-+sqrt%28+-15+%29%29%2F%282%281%29%29 Subtract 16 from 1 to get -15


x+=+%281+%2B-+sqrt%28+-15+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%281+%2B-+i%2Asqrt%2815%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%2815%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2815%29%29%2F%282%29 Break up the expression.


So the answers are x+=+%281%2Bi%2Asqrt%2815%29%29%2F%282%29 or x+=+%281-i%2Asqrt%2815%29%29%2F%282%29


which approximate to 0.5%2B1.936%2Ai or x=0.5-1.936%2Ai