The some of the squares of two consecutive integers is 145. find the integers.

The 2 numbers are 8 and 9.
8^2=64
9^2=81
81+64=145

X^2 + ( x + 1 )^2 = 145 ;
x^2 + x^2 +2x + 1 = 145 ;
2x^2 + 2x - 144 = 0 ;
x^2 + x - 72 = 0 ;
You solve the equation; the solutions of the equation are 8 and - 9 ( integers );
The two consecutive integers are 8 and 9 or - 9 and - 8 .