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

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.