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

Solution:

Let the required number be ‘x’.

Given that square of the number is 12 less than 7 times the number.

Let us express this statement as an algebraic expression.

⇒ x² = 7x -12

⇒ x² - 7x + 12 = 0

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

⇒ x² - 4x - 3x + 12 = 0

⇒ x(x - 4) - 3(x - 4) = 0

⇒ (x - 3)(x - 4)

⇒ x = 3 or 4

Substituting x = 3 in the equation x² = 7x -12,

3² = (7 × 3) - 12 = 9

Substituting x = 4 in the equation x² = 7x -12,

4² = (7 × 4) - 12 = 16

Since both the values satisfy the equation, x = 3 or 4.

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

Summary:

x = 3 or 4 satisfies the condition, given that the square of a number is 12 less than 7 times the number.