SOLUTION: what two numbers when multiplied equals 9000 and when added equals to negative 200

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Question 250367: what two numbers when multiplied equals 9000 and when added equals to negative 200
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
both numbers are negative because their product is positive but their sum is negative
n*m=9000
n+m=-200
n=-200-m
substitute -200-m for n in the first
(-200-m)*m=9000
-200m-m^2=9000
add -200m-m^2 to both sides
m^2+200m +9000=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B200x%2B9000+=+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=%28200%29%5E2-4%2A1%2A9000=4000.

Discriminant d=4000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-200%2B-sqrt%28+4000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28200%29%2Bsqrt%28+4000+%29%29%2F2%5C1+=+-68.3772233983162
x%5B2%5D+=+%28-%28200%29-sqrt%28+4000+%29%29%2F2%5C1+=+-131.622776601684

Quadratic expression 1x%5E2%2B200x%2B9000 can be factored:
1x%5E2%2B200x%2B9000+=+1%28x--68.3772233983162%29%2A%28x--131.622776601684%29
Again, the answer is: -68.3772233983162, -131.622776601684. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B200%2Ax%2B9000+%29