SOLUTION: Think of two numbers. When you add them you get 6.5. When you multiply you get 0.64. What are the two numbers.

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Question 784954: Think of two numbers. When you add them you get 6.5. When you multiply you get 0.64. What are the two numbers.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let the numbers be x and y.
x+y=6.5
xy=.64
.
x=6.5-y
y(6.5-y)=.64
6.5y-y^2=.64
-y^2+6.5y-.64=0
y=.1 and x=6.4 or vice versa (see below)
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B6.5x%2B-.64+=+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=%286.5%29%5E2-4%2A-1%2A-.64=39.69.

Discriminant d=39.69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6.5%2B-sqrt%28+39.69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286.5%29%2Bsqrt%28+39.69+%29%29%2F2%5C-1+=+0.1
x%5B2%5D+=+%28-%286.5%29-sqrt%28+39.69+%29%29%2F2%5C-1+=+6.4

Quadratic expression -1x%5E2%2B6.5x%2B-.64 can be factored:
-1x%5E2%2B6.5x%2B-.64+=+%28x-0.1%29%2A%28x-6.4%29
Again, the answer is: 0.1, 6.4. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B6.5%2Ax%2B-.64+%29