SOLUTION: a certain number is added to the square of the number results in 8.75.what is the number?

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Question 555067: a certain number is added to the square of the number results in 8.75.what is the number?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+x=8.75
x^2+x-8.75=0
x=-3.5, x=2.5 See below
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-8.75+=+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=%281%29%5E2-4%2A1%2A-8.75=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+36+%29%29%2F2%5C1+=+2.5
x%5B2%5D+=+%28-%281%29-sqrt%28+36+%29%29%2F2%5C1+=+-3.5

Quadratic expression 1x%5E2%2B1x%2B-8.75 can be factored:
1x%5E2%2B1x%2B-8.75+=+1%28x-2.5%29%2A%28x--3.5%29
Again, the answer is: 2.5, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-8.75+%29