1. **State the problem:** Solve the equation $$x^4 - 18x^2 + 81 = 0$$ to find the solution set. 2. **Rewrite the equation:** Notice that the equation is quadratic in form if we let $$y = x^2$$. Then the equation becomes: $$y^2 - 18y + 81 = 0$$ 3. **Solve the quadratic equation:** Use the quadratic formula: $$y = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $$a=1$$, $$b=-18$$, and $$c=81$$. 4. **Calculate the discriminant:** $$\Delta = (-18)^2 - 4 \times 1 \times 81 = 324 - 324 = 0$$ 5. **Find the roots for y:** $$y = \frac{18 \pm \sqrt{0}}{2} = \frac{18}{2} = 9$$ 6. **Back-substitute for x:** Since $$y = x^2$$, we have: $$x^2 = 9$$ 7. **Solve for x:** $$x = \pm \sqrt{9} = \pm 3$$ 8. **Final solution set:** $$\{3, -3\}$$ **Answer:** b. \{3, -3\}