What are the solutions to x² = -49?

Take the square root of both sides: $x=\pm\sqrt{-49}=\pm\sqrt{49}\cdot\sqrt{-1}=\pm7i$, choice B. Check: $(7i)^2=49i^2=-49$. Choice A ($\pm7$) squares to $+49$, not $-49$. Choice C ($\pm49i$) squares to $-2401$, because it forgets to take the square root of $49$. Choice D (no solution) is true only if we restrict to real numbers, but the complex numbers do contain solutions. Since the problem is stated in the setting of this exam's complex-number content, imaginary solutions are expected.