SOLUTION: a girl is 6years older than her brother.the product of their ages is 185 find their ages

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Question 756704: a girl is 6years older than her brother.the product of their ages is 185 find their ages
Answer by Alan3354(69443) About Me  (Show Source):
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a girl is 6years older than her brother.the product of their ages is 185 find their ages
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x*(x+6) = 185
x%5E2+%2B+6x+-+185+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B6x%2B-185+=+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%29%5E2-4%2A1%2A-185=776.

Discriminant d=776 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+776+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+776+%29%29%2F2%5C1+=+10.9283882771841
x%5B2%5D+=+%28-%286%29-sqrt%28+776+%29%29%2F2%5C1+=+-16.9283882771841

Quadratic expression 1x%5E2%2B6x%2B-185 can be factored:
1x%5E2%2B6x%2B-185+=+%28x-10.9283882771841%29%2A%28x--16.9283882771841%29
Again, the answer is: 10.9283882771841, -16.9283882771841. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-185+%29

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He's 10.928
She's 16.928