SOLUTION: what is the exact and approximate solution to three decimal places x^2+5x-7=0

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Question 299526: what is the exact and approximate solution to three decimal places x^2+5x-7=0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
what is the exact and approximate solution to three decimal places x^2+5x-7=0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%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=%285%29%5E2-4%2A1%2A-7=53.

Discriminant d=53 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+53+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+53+%29%29%2F2%5C1+=+1.14005494464026
x%5B2%5D+=+%28-%285%29-sqrt%28+53+%29%29%2F2%5C1+=+-6.14005494464026

Quadratic expression 1x%5E2%2B5x%2B-7 can be factored:
1x%5E2%2B5x%2B-7+=+%28x-1.14005494464026%29%2A%28x--6.14005494464026%29
Again, the answer is: 1.14005494464026, -6.14005494464026. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-7+%29