SOLUTION: How do you solve: x^2+4x=10

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Question 513668: How do you solve: x^2+4x=10
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
How do you solve: x^2+4x=10
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Use the quadratic equation.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B4x%2B-10+=+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=%284%29%5E2-4%2A1%2A-10=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+56+%29%29%2F2%5C1+=+1.74165738677394
x%5B2%5D+=+%28-%284%29-sqrt%28+56+%29%29%2F2%5C1+=+-5.74165738677394

Quadratic expression 1x%5E2%2B4x%2B-10 can be factored:
1x%5E2%2B4x%2B-10+=+%28x-1.74165738677394%29%2A%28x--5.74165738677394%29
Again, the answer is: 1.74165738677394, -5.74165738677394. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-10+%29

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x = -2 ± sqrt(14)