Question

If \(x^2-x=12\), then which of the following could be the value of \(x^2\) ? A. 1 B. 9 C. 36 D. 144

Short answer

The correct answer is B. 9.

Step-by-step solution

Rearrange the equation

First, let's rewrite the equation to make it easier to solve. We can add "x" to both sides of the equation to get: \(x^2 - x + x = 12 + x\) Which simplifies to: \(x^2 = 12 + x\)

Find the possible values of x

Now, we will find the possible values of x. To do this, we can either factor the equation, use the quadratic formula, or use trial and error. In this case, let's use trial and error. We will plug in the given answer choices for \(x^2\) and see which one satisfies the equation: A. If \(x^2 = 1\), then \(x = \pm 1\). Plugging that into the equation: \((1)^2 = 12 + 1\) which is not true. \((-1)^2 = 12 - 1\) which is also not true. B. If \(x^2 = 9\), then \(x = \pm 3\). Plugging that into the equation: \((3)^2 = 12 + 3\) which is true. \((-3)^2 = 12 - 3\) which is not true. C. If \(x^2 = 36\), then \(x = \pm 6\). Plugging that into the equation: \((6)^2 = 12 + 6\) which is not true. \((-6)^2 = 12 - 6\) which is also not true. D. If \(x^2 = 144\), then \(x = \pm 12\). Plugging that into the equation: \((12)^2 = 12 + 12\) which is not true. \((-12)^2 = 12 - 12\) which is also not true.

Identify the correct answer

Out of all the given answer choices, only choice B satisfied the equation when \(x = 3\). Therefore, the correct answer is B. 9.