Choice C is the correct answer. To solve $x^2 = k$, take the square root of both sides. Crucially, you must include both the positive and negative roots.

$x = \pm \sqrt{100} = \pm 10$.

Choice A is incorrect because it misses the negative solution ($-10 \times -10 = 100$ too). Choice B is incorrect because it divides by 2 instead of taking the square root. Choice D is incorrect because it divides by 2 and adds $\pm$.