SOLUTION: solve for x: x^2-x=7

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Question 545809: solve for x: x^2-x=7
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-x-7=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-7+=+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=%28-1%29%5E2-4%2A1%2A-7=29.

Discriminant d=29 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+29+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+29+%29%29%2F2%5C1+=+3.19258240356725
x%5B2%5D+=+%28-%28-1%29-sqrt%28+29+%29%29%2F2%5C1+=+-2.19258240356725

Quadratic expression 1x%5E2%2B-1x%2B-7 can be factored:
1x%5E2%2B-1x%2B-7+=+1%28x-3.19258240356725%29%2A%28x--2.19258240356725%29
Again, the answer is: 3.19258240356725, -2.19258240356725. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-7+%29