SOLUTION: what are two numbers that multiply to make -56 and add to make -6?

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Question 737620: what are two numbers that multiply to make -56 and add to make -6?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
what are two numbers that multiply to make -56 and add to make -6?
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x*y = -56
x + y = -6
y = -x -6
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x*(-x-6) = -56
x%5E2+%2B+6x+=+56
x%5E2+%2B+6x+-+56+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-56+=+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=%286%29%5E2-4%2A1%2A-56=260.

Discriminant d=260 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+260+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+260+%29%29%2F2%5C1+=+5.06225774829855
x%5B2%5D+=+%28-%286%29-sqrt%28+260+%29%29%2F2%5C1+=+-11.0622577482985

Quadratic expression 1x%5E2%2B6x%2B-56 can be factored:
1x%5E2%2B6x%2B-56+=+%28x-5.06225774829855%29%2A%28x--11.0622577482985%29
Again, the answer is: 5.06225774829855, -11.0622577482985. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-56+%29

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The 2 solutions are the 2 numbers.