1. **State the problem:** Solve the quadratic equation $$x^2 - 6x = -9$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 - 6x + 9 = 0$$ 3. **Recognize the form:** The equation is a perfect square trinomial: $$x^2 - 6x + 9 = (x - 3)^2$$ 4. **Solve the equation:** Set the square equal to zero: $$(x - 3)^2 = 0$$ 5. **Find the root:** $$x - 3 = 0 \implies x = 3$$ 6. **Conclusion:** The solution set is $$\{3\}$$. **Answer:** B. {3}