SOLUTION: What two numbers when multiplied together equal, -11250, When added together = 125

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Question 1015549: What two numbers when multiplied together equal, -11250,
When added together = 125
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
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A and B are the two numbers
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A+B=125
A=125-B
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AB=-11250
%28125-B%29%28B%29=-11250
-B%5E2%2B125B=-11250
-B%5E2%2B125B%2B11250=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aB%5E2%2BbB%2Bc=0 (in our case -1B%5E2%2B125B%2B11250+=+0) has the following solutons:

B%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=%28125%29%5E2-4%2A-1%2A11250=60625.

Discriminant d=60625 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-125%2B-sqrt%28+60625+%29%29%2F2%5Ca.

B%5B1%5D+=+%28-%28125%29%2Bsqrt%28+60625+%29%29%2F2%5C-1+=+-60.6107225224513
B%5B2%5D+=+%28-%28125%29-sqrt%28+60625+%29%29%2F2%5C-1+=+185.610722522451

Quadratic expression -1B%5E2%2B125B%2B11250 can be factored:
-1B%5E2%2B125B%2B11250+=+-1%28B--60.6107225224513%29%2A%28B-185.610722522451%29
Again, the answer is: -60.6107225224513, 185.610722522451. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B125%2Ax%2B11250+%29

B=-60.6107 or 185.6107
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A=125-(-60.6107)=185.6107
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ANSWER: The two numbers are 185.6107 and -60.6107.
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CHECK:
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AB=-11250
(185.6107)(-60.6107)=-11250
11249.9945=11250 (error due to rounding roots)