SOLUTION: Find two consecutive positive intergers such that the sum of their square is 85 This problem has confused me by adding in square, how do I go about solving this type of problem?

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Question 65708: Find two consecutive positive intergers such that the sum of their square is 85
This problem has confused me by adding in square, how do I go about solving this type of problem?
Found 2 solutions by Nate, funmath:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
First Integer = i
Second Integer = i + 1
(i)^2 + (i + 1)^2 = 85
i^2 + i^2 + 2i + 1 = 85
2i^2 + 2i = 84
i^2 + i = 42
(i + 0.5)^2 = 42.25
i = -0.5 +- 6.5
i = -7 or i = 6
6 and 7

Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Find two consecutive positive intergers such that the sum of their square is 85
Let the first integer be: x
Then the next consecutive integer is: x+1
Sum means add.
Square means raise to the second power
is means =.
x%5E2%2B%28x%2B1%29%5E2=85
x%5E2%2Bx%5E2%2B2x%2B1=85
2x%5E2%2B2x%2B1=85
2x%5E2%2B2x%2B1-85=85-85
2x%5E2%2B2x-84=0
2%28x%5E2%2Bx-42%29=0
2%28x%5E2%2Bx-42%29%2F2=0%2F2
x%5E2%2Bx-42=0
(x+7)(x-6)=0
x+7=0 or x-6=0
x+7-7=0-7 or x-6+6=0+6
x=-7 or x=6
Since you were asked for two consecutive POSITIVE integers
The first integer is: x=6
and the second is: x+1=6+1=7
:
Sanity check:
are 6 and 7 consecutive integers? Yes!
Do the sum of their squares=85?
6^2+7^2=85
36+49=85
85=85 Yes!
It appears that we're sane...for now.
Happy Calculating!!!