Question

The square of a number exceeds the number by 72. Find the number

Answer 1

X^2 = x + 72 you have a quadratic.
x^2 - x - 72 = 0
(x - 9)*(x + 8) = 0
x = 9 or x = - 8

We have to check this one. One of the answers could be wrong.
9^2 = 9 + 72
81 = 81 This one checks out and is OK.

(-8)^2 = -8 + 72
64 = - 8 + 72 
64 = 64.
Both answers work.