SOLUTION: factor completely: 44b^2-108b-72 showing all work

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Question 798406: factor completely: 44b^2-108b-72 showing all work
Answer by Alan3354(69443) About Me  (Show Source):
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factor completely: 44b^2-108b-72 showing all work
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Divide by 4
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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 11x%5E2%2B-27x%2B-18+=+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=%28-27%29%5E2-4%2A11%2A-18=1521.

Discriminant d=1521 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--27%2B-sqrt%28+1521+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-27%29%2Bsqrt%28+1521+%29%29%2F2%5C11+=+3
x%5B2%5D+=+%28-%28-27%29-sqrt%28+1521+%29%29%2F2%5C11+=+-0.545454545454545

Quadratic expression 11x%5E2%2B-27x%2B-18 can be factored:
11x%5E2%2B-27x%2B-18+=+%28x-3%29%2A%28x--0.545454545454545%29
Again, the answer is: 3, -0.545454545454545. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+11%2Ax%5E2%2B-27%2Ax%2B-18+%29

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Other than the 4, it can't be factored.
= 4%2A%2811b%5E2+-+27b+-+18%29