SOLUTION: if the product is 120 and the sum is 50 what are the two numbers

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Question 377749: if the product is 120 and the sum is 50 what are the two numbers
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x*(50-x) = 120
x%5E2+-+50x+%2B+120+=+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-50x%2B120+=+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=%28-50%29%5E2-4%2A1%2A120=2020.

Discriminant d=2020 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+2020+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+2020+%29%29%2F2%5C1+=+47.4722050542442
x%5B2%5D+=+%28-%28-50%29-sqrt%28+2020+%29%29%2F2%5C1+=+2.52779494575577

Quadratic expression 1x%5E2%2B-50x%2B120 can be factored:
1x%5E2%2B-50x%2B120+=+%28x-47.4722050542442%29%2A%28x-2.52779494575577%29
Again, the answer is: 47.4722050542442, 2.52779494575577. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-50%2Ax%2B120+%29

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--> 25 ± sqrt(505)
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I suspect a typo.