SOLUTION: Solve by using the quadratic formula. x^2 = –x + 4

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Question 104966: Solve by using the quadratic formula. x^2 = –x + 4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+=+-x+%2B+4 Start with the given equation


+0=-x%5E2+-x+%2B+4 Subtract x%5E2 from both sides

Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve -x%5E2-x%2B4=0 ( notice a=-1, b=-1, and c=4)





x+=+%28--1+%2B-+sqrt%28+%28-1%29%5E2-4%2A-1%2A4+%29%29%2F%282%2A-1%29 Plug in a=-1, b=-1, and c=4




x+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%2A-1%2A4+%29%29%2F%282%2A-1%29 Negate -1 to get 1




x+=+%281+%2B-+sqrt%28+1-4%2A-1%2A4+%29%29%2F%282%2A-1%29 Square -1 to get 1 (note: remember when you square -1, you must square the negative as well. This is because %28-1%29%5E2=-1%2A-1=1.)




x+=+%281+%2B-+sqrt%28+1%2B16+%29%29%2F%282%2A-1%29 Multiply -4%2A4%2A-1 to get 16




x+=+%281+%2B-+sqrt%28+17+%29%29%2F%282%2A-1%29 Combine like terms in the radicand (everything under the square root)




x+=+%281+%2B-+sqrt%2817%29%29%2F%282%2A-1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%281+%2B-+sqrt%2817%29%29%2F-2 Multiply 2 and -1 to get -2


So now the expression breaks down into two parts


x+=+%281+%2B+sqrt%2817%29%29%2F-2 or x+=+%281+-+sqrt%2817%29%29%2F-2



Now break up the fraction



x=%2B1%2F-2%2Bsqrt%2817%29%2F-2 or x=%2B1%2F-2-sqrt%2817%29%2F-2



Simplify



x=-1%2F2-sqrt%2817%29%2F2 or x=-1%2F2%2Bsqrt%2817%29%2F2



So the solutions are:

x=-1%2F2-sqrt%2817%29%2F2 or x=-1%2F2%2Bsqrt%2817%29%2F2