The difference of a number and its square is 182. Find the number.

The answer would be 196.

The square root of 196 is 14 and 196-14=182.

Let x be the number

⇒ x² - x = 182

by transposition

x² - x - 182 = 0

this can be written as

x² - 14x + 13x - 182 = 0

by factorisation

x (x - 14) + 13 (x - 14) = 0

(x - 14) (x + 13) = 0

∴ x = 14 OR x = - 13.

Therefore the number is 14.