SOLUTION: Solve the equation: x^-2 - 15x^-1 + 44 = 0

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Question 144509: Solve the equation:
x^-2 - 15x^-1 + 44 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E-2+-+15x%5E-1+%2B+44+=+0
Multiply by x^2
1+-+15x+%2B+44x%5E2+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 44x%5E2%2B-15x%2B1+=+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=%28-15%29%5E2-4%2A44%2A1=49.

Discriminant d=49 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--15%2B-sqrt%28+49+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-15%29%2Bsqrt%28+49+%29%29%2F2%5C44+=+0.25
x%5B2%5D+=+%28-%28-15%29-sqrt%28+49+%29%29%2F2%5C44+=+0.0909090909090909

Quadratic expression 44x%5E2%2B-15x%2B1 can be factored:
44x%5E2%2B-15x%2B1+=+%28x-0.25%29%2A%28x-0.0909090909090909%29
Again, the answer is: 0.25, 0.0909090909090909. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+44%2Ax%5E2%2B-15%2Ax%2B1+%29


x = 0.25, x=1/11