SOLUTION: Solve by the quadratic formula: x^2 = -8x + 1

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Question 384607: Solve by the quadratic formula: x^2 = -8x + 1
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
x^2 = -8x + 1
x^2 + 8x = 1
x^2 + 8x - 1 = 0
.
applying the quadratic formula yields:
x = {0.123, -8.123}
.
Details follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B8x%2B-1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%288%29%5E2-4%2A1%2A-1=68.

Discriminant d=68 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+68+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+68+%29%29%2F2%5C1+=+0.123105625617661
x%5B2%5D+=+%28-%288%29-sqrt%28+68+%29%29%2F2%5C1+=+-8.12310562561766

Quadratic expression 1x%5E2%2B8x%2B-1 can be factored:
1x%5E2%2B8x%2B-1+=+1%28x-0.123105625617661%29%2A%28x--8.12310562561766%29
Again, the answer is: 0.123105625617661, -8.12310562561766. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B8%2Ax%2B-1+%29