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

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: \(x^2 = 12 + x\)

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.

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