Answer: D

Small Hint:

Let $x^2 - 5$ be the quantity being squared

Big Hint:

Solve $x^2 - 5 = 4$ and $x^2 - 5 = -4$

Video solution:

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Written solution:

Recall that $$a^2 - b^2 = (a + b)(a - b).$$ We can do the following rearrangement. $$\begin{aligned} (x^2 - 5)^2 - 4^2 &= 0 \\ (x^2 - 1)(x^2 - 9) &= 0 \end{aligned}$$

From this we can see that there are $4$ possible values for $x.$

Thus, the correct answer is D.