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

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.

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