Let n be a postive integer, then n+1 is the next integer.

sum the squares of those noumbers:
n^2 + n^2 + 2n +1=85

solve for n.

so this is what i did.

n^2+2n+1=85
n^2+2n=85-1
n^2+2n=84
n=7056+4n

To solve the equation n^2 + 2n + 1 = 85 for n:

1. First, bring all terms to one side of the equation:
n^2 + 2n - 84 = 0

2. This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = 2, and c = -84.

3. To factor the equation, find two numbers that multiply to give ac (a*c = 1 * -84 = -84) and add up to give b (2).
The two numbers in this case are 12 and -7 because 12 * -7 = -84 and 12 + (-7) = 2.

4. Rewrite the quadratic equation using the factored form:
(n + 12)(n - 7) = 0

5. Set each factor equal to zero and solve for n:
n + 12 = 0 --> n = -12
n - 7 = 0 --> n = 7

Therefore, the values of n that satisfy the equation are n = -12 and n = 7.