SOLUTION: Solve x^2+18x+32+=226

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Question 204793: Solve x^2+18x+32+=226
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+18x+32=226
x^2+18x-194=0
x=-9+5sqrt(11), x=-9-5sqrt(11) 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%2B18x%2B-194+=+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=%2818%29%5E2-4%2A1%2A-194=1100.

Discriminant d=1100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+1100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+1100+%29%29%2F2%5C1+=+7.583123951777
x%5B2%5D+=+%28-%2818%29-sqrt%28+1100+%29%29%2F2%5C1+=+-25.583123951777

Quadratic expression 1x%5E2%2B18x%2B-194 can be factored:
1x%5E2%2B18x%2B-194+=+1%28x-7.583123951777%29%2A%28x--25.583123951777%29
Again, the answer is: 7.583123951777, -25.583123951777. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B18%2Ax%2B-194+%29