SOLUTION: I have asked this question within the past two days without a response. I am having a tough time figuring out how to set this problem up. Once I know how to set it up and why, I ca

Question 68069: I have asked this question within the past two days without a response. I am having a tough time figuring out how to set this problem up. Once I know how to set it up and why, I can probably solve the equation. I hope someone out there can help me with this one, please.
Find two consecutive positive integers such that the sum of their squares is 85. [You must use algebra to solve this, setting up an equation with a variable, and using algebra to solve for the variable.]
Found 2 solutions by Earlsdon, checkley71:
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let x be the first positive integer. The next consecutive positive integer would then be x+1.
The sum of the squares of these is 85.
Simplify and solve for x.
Simplify.
Subtract 85 from both sides.
Divide through by 2.
Factor.
Apply the zero product principle.
and/or
So, x = -7 and x = 6 Discard the negative value as the problem requires positive integers.
The two integers are: 6 and 7
Check:
=

Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
let x^2 be the first number & (x+1)^2 the next number
x^2+(x+1)^2=85
x^2+x^2+2x+1=85
2x^2+2x+1-85
2x^2+2x-84=0
x^2+x^2-42=0
(x+7)(x-6)=0
x-6=0
x=6 answer for the first number
6+1=7 for the next number.
proof
6^2+7^2=84
36+49=84
84=84

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