# The square of a number is 12 less than 7 times the number. What is the number?

Let us find the required number.

## Answer: The number can be 3 or 4 which satisfies the condition that the square of a number is 12 less than 7 times the number.

The problem can be solved by expressing the given data as a mathematical expression and try to solve thus obtained equation.

**Explanation:**

Let the required number be x

The given information is that the square of a number is 12 less than 7 times the number.

⇒ x^{2} = 7x - 12

⇒ x^{2} - 7x + 12 = 0

Let us solve the quadratic equation by splitting the middle term:

⇒ x^{2} - 4x - 3x + 12 = 0

⇒ x(x - 4) - 3(x - 4) = 0

⇒ (x - 4)(x - 3) = 0

⇒ x = 4 or x = 3

As 4^{2 }= 7(4) - 12 it satisfies as well as 3^{2 }= 7(3) - 12