SOLUTION: what is a factor of -252 whose sum is 29

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Question 480979: what is a factor of -252 whose sum is 29
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
It takes at least 2 to make a sum.
36 & -7
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You can do it the hard way:
x*(29 - x) = -252
-x%5E2+%2B+29x+%2B+252+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B29x%2B252+=+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=%2829%29%5E2-4%2A-1%2A252=1849.

Discriminant d=1849 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-29%2B-sqrt%28+1849+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2829%29%2Bsqrt%28+1849+%29%29%2F2%5C-1+=+-7
x%5B2%5D+=+%28-%2829%29-sqrt%28+1849+%29%29%2F2%5C-1+=+36

Quadratic expression -1x%5E2%2B29x%2B252 can be factored:
-1x%5E2%2B29x%2B252+=+%28x--7%29%2A%28x-36%29
Again, the answer is: -7, 36. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B29%2Ax%2B252+%29