Let the positive integer be x
The sum of the positive integer and its square is 90:
x + x² = 90
x² + x - 90 = 0
Solve the quadratic equation by factoring:
(x + 10) (x - 9) = 0
x + 10 = 0 x - 9 = 0
x = -10 x = 9
Choose the positive root, x= 9.
The positive integer is 9.
To check:
x + x² = 90
9 + (9)² = 90
9 + 81 = 90
90 = 90
