SOLUTION: The sum of two real numbers is 18 and the product is 70. What are the two numbers?

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Question 890251: The sum of two real numbers is 18 and the product is 70. What are the two numbers?
Answer by Alan3354(69443) About Me  (Show Source):
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The sum of two real numbers is 18 and the product is 70. What are the two numbers?
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x*(18-x) = 70
x%5E2+-+18x+%2B+70+=+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-18x%2B70+=+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=%28-18%29%5E2-4%2A1%2A70=44.

Discriminant d=44 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--18%2B-sqrt%28+44+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-18%29%2Bsqrt%28+44+%29%29%2F2%5C1+=+12.3166247903554
x%5B2%5D+=+%28-%28-18%29-sqrt%28+44+%29%29%2F2%5C1+=+5.6833752096446

Quadratic expression 1x%5E2%2B-18x%2B70 can be factored:
1x%5E2%2B-18x%2B70+=+%28x-12.3166247903554%29%2A%28x-5.6833752096446%29
Again, the answer is: 12.3166247903554, 5.6833752096446. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-18%2Ax%2B70+%29

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