Choice B is the correct answer. Before taking the square root, isolate the squared term.

1. Divide both sides by 2: $x^2 = 25$.
2. Take the square root of both sides: $x = \pm \sqrt{25}$.
3. Solve: $x = \pm 5$.

Choice A is incorrect because it forgets to take the square root. Choice C is incorrect because it forgets to take the square root of 25. Choice D is incorrect because it misses the negative solution.