SOLUTION: Find two numbers such that their sum is 302 and their product is 189.

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Question 913704: Find two numbers such that their sum is 302 and their product is 189.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x(302-x) = 189
302x - x^2 = 189
x^2 -302x + 189 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-302x%2B189+=+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=%28-302%29%5E2-4%2A1%2A189=90448.

Discriminant d=90448 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--302%2B-sqrt%28+90448+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-302%29%2Bsqrt%28+90448+%29%29%2F2%5C1+=+301.372869893475
x%5B2%5D+=+%28-%28-302%29-sqrt%28+90448+%29%29%2F2%5C1+=+0.627130106524874

Quadratic expression 1x%5E2%2B-302x%2B189 can be factored:
1x%5E2%2B-302x%2B189+=+1%28x-301.372869893475%29%2A%28x-0.627130106524874%29
Again, the answer is: 301.372869893475, 0.627130106524874. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-302%2Ax%2B189+%29