Question 60835
Let the two consecutive integer be x and x +1
Sum of their squares is 85.
That means 
x^2 +( x +1)^2 = 85
x^2 +x^2 + 1 + 2x = 85
2x^2 +2x  = 85 -1
2x^2 + 2x  = 84
2x^2 + 2x -84 =0
Divide the above equation by 2, we get
x^2 +x - 42 = 0
x^2 + 7x -6x – 42 =0
x(x +7) – 6 (x +7) = 0
(x - 6) (x + 7) = 0
x  - 6 = 0  or x +  7 = 0
x = 6 or  -7

So when x = 6, we get (x+1) = 6 +1 = 7
So when x =-7, (x +1) = - 7 + 1 = - 6

Therefore the consecutive numbers are 6,7 and -7 , 6