1. **State the problem:** Solve the equation $$d^2 - 24 = 0$$ for $d$. 2. **Formula and rules:** This is a quadratic equation in the form $$d^2 = 24$$. To solve for $d$, we take the square root of both sides. 3. **Isolate the variable:** Add 24 to both sides: $$d^2 - 24 + 24 = 0 + 24$$ $$d^2 = 24$$ 4. **Take the square root:** $$d = \pm \sqrt{24}$$ 5. **Simplify the square root:** $$\sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6}$$ 6. **Final answer:** $$d = \pm 2\sqrt{6}$$