Question

the square of a number is 12 less than 7 times the number. what is the number?
-4 or -3
-4 or 3
-3 or 4
3 or 4

Explanation:

Step1: Define the variable

Let the number be \( x \).

Step2: Translate the problem into an equation

The square of the number is \( x^2 \), and 7 times the number is \( 7x \). The square of the number is 12 less than 7 times the number, so the equation is \( x^2 = 7x - 12 \).

Step3: Rearrange the equation to standard quadratic form

Subtract \( 7x \) and add 12 to both sides to get \( x^2 - 7x + 12 = 0 \).

Step4: Factor the quadratic equation

We need two numbers that multiply to 12 and add up to -7. Those numbers are -3 and -4. So, the factored form is \( (x - 3)(x - 4) = 0 \).

Step5: Solve for \( x \)

Set each factor equal to zero: \( x - 3 = 0 \) gives \( x = 3 \), and \( x - 4 = 0 \) gives \( x = 4 \).

Answer:

3 or 4