Question 88630
Find two consecutive integers such that the sum of their squares is 85.
I have gotten this far:

n^2 + (n+1)^2 = 85 
:
to continue, FOIL (n+1)(n+1)
n^2 + (n^2 + 2n + 1) = 85
:
n^2 + n^2 + 2n + 1 - 85 = 0: subtract 85 from both sides:
:
2n^2 + 2n - 84 = 0; combine like terms, you have a quadratic equation
:
n^2 + n - 42 = 0; simplify, divide equation (each term) by 2
:
(n+7)(n-6) = 0; factors easily:
:
n = -7 
and 
n = +6
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Both these solutions will work, here's x = -7
(-7^2) + (-6^2) =
 +49 + 36 = 85
:
:
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