Question

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

Answer 1

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.

Answer 2

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