Question

If a number is increased by its square, the result is 72 find the number

Answer 1

Translating into a mathematical equation:

n + n^2 = 72

Rewriting,    n^2 + n - 72 = 0
Factoring,    (n+9)(n-8) = 0
Solving for n:  n = -9 or n = 8

You must check both answers before accepting one, the other or both.

Example:  suppose we check out n = 8.  Then  8 + 8^2 = 72 is true, and n = 8 is a solution.  Is n = -9 a solution?  Try it.