SOLUTION: Find two consecutive integers that have a product of 182.

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Question 750907: Find two consecutive integers that have a product of 182.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x(x+1) = 182

x^2 + x = 182

x^2 + x - 182 = 0

Use the quadratic formula to solve for x

x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x+=+%28-%281%29%2B-sqrt%28%281%29%5E2-4%281%29%28-182%29%29%29%2F%282%281%29%29 Plug in a+=+1, b+=+1, c+=+-182

x+=+%28-1%2B-sqrt%281-%28-728%29%29%29%2F%282%29

x+=+%28-1%2B-sqrt%281%2B728%29%29%2F%282%29

x+=+%28-1%2B-sqrt%28729%29%29%2F2

x+=+%28-1%2Bsqrt%28729%29%29%2F2 or x+=+%28-1-sqrt%28729%29%29%2F2

x+=+%28-1%2B27%29%2F2 or x+=+%28-1-27%29%2F2

x+=+26%2F2 or x+=+-28%2F2

x+=+13 or x+=+-14

So the two numbers are either

13 and 14

or

-14 and -13