To solve the equation \( 3x^2 = -72 \), we start by isolating \( x^2 \):
\[ x^2 = -\frac{72}{3} = -24 \]
Next, we take the square root of both sides. Since the right side is negative, we will involve imaginary numbers:
\[ x = \pm \sqrt{-24} = \pm \sqrt{24} i \]
We can simplify \( \sqrt{24} \):
\[ \sqrt{24} = \sqrt{4 \cdot 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6} \]
Thus, the solutions for \( x \) are:
\[ x = \pm 2\sqrt{6} i \]
Now, let's determine which option corresponds to our solution, \( \pm 2i\sqrt{6} \):
- A: \( \pm 26\pm 2\sqrt{6} \) (not equivalent)
- B: \( \pm 6i\sqrt{2} \) (not equivalent)
- C: \( -24 \) (not equivalent)
- D: \( \pm 2i\sqrt{6} \) (this matches our result)
Therefore, the correct answer is:
D \( \pm 2i\sqrt{6} \).