SOLUTION: Find 2 real numbers that differ from 8 and has a product of 54

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Question 890820: Find 2 real numbers that differ from 8 and has a product of 54
Answer by Alan3354(69443) About Me  (Show Source):
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Find 2 real numbers that differ from 8 and has a product of 54
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x - y = 8
x*y = 54
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y = x - 8
x*(x-8) = 54
x%5E2+-+8x+-+54+=+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-9x%2B-54+=+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=%28-9%29%5E2-4%2A1%2A-54=297.

Discriminant d=297 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+297+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+297+%29%29%2F2%5C1+=+13.116843969807
x%5B2%5D+=+%28-%28-9%29-sqrt%28+297+%29%29%2F2%5C1+=+-4.11684396980704

Quadratic expression 1x%5E2%2B-9x%2B-54 can be factored:
1x%5E2%2B-9x%2B-54+=+%28x-13.116843969807%29%2A%28x--4.11684396980704%29
Again, the answer is: 13.116843969807, -4.11684396980704. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B-54+%29

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