The square of 9 less than a number is 3 less than the number. What is the number?

Solution: 

Let us convert the given statement into an algebraic equation.

Let the required number be ‘x’.

(x - 9)² = x - 3

Using the formula (a - b)² = a² -2ab + b²

x² - 18x + 81 = x - 3

x² - 19x + 84 = 0

x² - 12x - 7x + 84 = 0 [by splitting the terms, and taking the common factor out, we get]

x(x -12) - 7(x - 12) = 0

(x - 12)(x - 7) = 0

x = 12 or 7

The square of 9 less than a number is 3 less than the number. What is the number?

Summary: 

The required number if the square of 9 less than a number is 3 less than the number, is 12 or 7.