SOLUTION: Find two consecutive integers such that the sum of their squares is 61

Smaller consecutive integer = N
Larger consecutive integer N+!

sum of their squares is 61

          N² + (N+1)² = 61

      N² + (N+1)(N+1) = 61

N² + (N² + N + N + 1) = 61

     N² + N² + 2N + 1 = 61

         2N² + 2N + 1 = 61

Get 0 on the right:

        2N² + 2N - 60 = 0

Divide every term by 2

         N² +  N - 30 = 0
 
Factor:

       (N + 6)(N - 5) = 0

Use zero factor principle:

      N + 6 = 0;    N - 5 = 0
          N = -6        N = 5



Using answer N = -6
Smaller consecutive integer = N = -6
Larger consecutive integer N+1 = -6+1 = -5

Using answer N = 5
Smaller consecutive integer = N = 5
Larger consecutive integer N+1 = 5+1 = 6

Two answers:  -6 and -5,   or 5 and 6

Edwin