# 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} = a^{2} -2ab + b^{2}

x^{2} - 18x + 81 = x - 3

x^{2} - 19x + 84 = 0

x^{2} - 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.

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