SOLUTION: What two numbers multiply to -16 and adds to 8

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Question 963294: What two numbers multiply to -16 and adds to 8
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What two numbers multiply to -16 and adds to 8
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x*y = -16
x + y = 8 --> y = 8-x
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x(8-x) = -16
x%5E2+-+8x+-+16+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-8x%2B-16+=+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=%28-8%29%5E2-4%2A1%2A-16=128.

Discriminant d=128 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--8%2B-sqrt%28+128+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-8%29%2Bsqrt%28+128+%29%29%2F2%5C1+=+9.65685424949238
x%5B2%5D+=+%28-%28-8%29-sqrt%28+128+%29%29%2F2%5C1+=+-1.65685424949238

Quadratic expression 1x%5E2%2B-8x%2B-16 can be factored:
1x%5E2%2B-8x%2B-16+=+%28x-9.65685424949238%29%2A%28x--1.65685424949238%29
Again, the answer is: 9.65685424949238, -1.65685424949238. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-8%2Ax%2B-16+%29

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