SOLUTION: WHAT TWO NUMBERS WHEN MULTIPLIED THEIR SUM IS 120, AND WHEN ADDED THEIR SUM IS 28?

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Question 478219: WHAT TWO NUMBERS WHEN MULTIPLIED THEIR SUM IS 120, AND WHEN ADDED THEIR SUM IS 28?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
x*y = 120
x + y = 28
y = 28-x
---------------
x*(28-x) = 120
x%5E2+-28x+%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-28x%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=%28-28%29%5E2-4%2A1%2A120=304.

Discriminant d=304 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--28%2B-sqrt%28+304+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-28%29%2Bsqrt%28+304+%29%29%2F2%5C1+=+22.7177978870813
x%5B2%5D+=+%28-%28-28%29-sqrt%28+304+%29%29%2F2%5C1+=+5.28220211291865

Quadratic expression 1x%5E2%2B-28x%2B120 can be factored:
1x%5E2%2B-28x%2B120+=+%28x-22.7177978870813%29%2A%28x-5.28220211291865%29
Again, the answer is: 22.7177978870813, 5.28220211291865. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-28%2Ax%2B120+%29