SOLUTION: The product of two consecutive even intergers is 74.

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Question 229735: The product of two consecutive even intergers is 74.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
that's not possible, 74 = 2*37
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n*(n+2) = 74
n^2 + 2n - 74 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-74+=+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=%282%29%5E2-4%2A1%2A-74=300.

Discriminant d=300 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+300+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+300+%29%29%2F2%5C1+=+7.66025403784439
x%5B2%5D+=+%28-%282%29-sqrt%28+300+%29%29%2F2%5C1+=+-9.66025403784439

Quadratic expression 1x%5E2%2B2x%2B-74 can be factored:
1x%5E2%2B2x%2B-74+=+%28x-7.66025403784439%29%2A%28x--9.66025403784439%29
Again, the answer is: 7.66025403784439, -9.66025403784439. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-74+%29

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No integer solution.
Only one 'r' in integer, too.