SOLUTION: x^2 - 10x = -23

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Question 301417: x^2 - 10x = -23
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-10x=-23
x%5E2-10x%2B23=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-10x%2B23+=+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=%28-10%29%5E2-4%2A1%2A23=8.

Discriminant d=8 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+8+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+8+%29%29%2F2%5C1+=+6.41421356237309
x%5B2%5D+=+%28-%28-10%29-sqrt%28+8+%29%29%2F2%5C1+=+3.58578643762691

Quadratic expression 1x%5E2%2B-10x%2B23 can be factored:
1x%5E2%2B-10x%2B23+=+1%28x-6.41421356237309%29%2A%28x-3.58578643762691%29
Again, the answer is: 6.41421356237309, 3.58578643762691. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B23+%29