SOLUTION: Find two consecutive integers such that the sum of their squares is 85. Find all such integers.

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Question 680895: Find two consecutive integers such that the sum of their squares is 85. Find all such integers.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
The 2 consecutive numbers are x and x+1
So the question in words is the same as below equation:
%28x%5E2%29%2B%28x%2B1%29%5E2=85
x%5E2%2Bx%5E2%2B2x%2B1=85
Add and simplify
2x%28x%2B1%29%2B1=85
Subtract 1 from both sides
2x%28x%2B1%29=84
Divide by 2
x%28x%2B1%29=42
Distribute
x%5E2%2Bx=42
Subtract 42
x%5E2%2Bx-42=0
Find 2 numbers that add together that get 1 and multiply to get -42
They are 7 and -6
%28x%2B7%29%28x-6%29=0
X= -7 , 6
So 2 possible answers
(-7 and -6) or (6 and 7)
Check
6%5E2%2B7%5E2=85
36%2B49=85
85=85