1. Stating the problem: We need to solve $$(x-2)^2 = 9$$ using the factorization method. 2. Start by rewriting the equation: $$(x-2)^2 - 9 = 0$$. 3. Recognize this as a difference of squares: $$a^2 - b^2 = (a-b)(a+b)$$ where $$a = (x-2)$$ and $$b = 3$$. 4. Factor the left side: $$((x-2) - 3)((x-2) + 3) = 0$$. 5. Simplify each factor: $$(x-2 - 3)(x-2 + 3) = (x-5)(x+1) = 0$$. 6. Solve each factor by setting them equal to zero: - $$x-5=0$$ gives $$x=5$$ - $$x+1=0$$ gives $$x=-1$$ 7. Final solution: $$x=5$$ or $$x=-1$$.