1. The problem asks us to complete the square for the polynomial $$x^2 - 6x + \_\_\_$$ to make it a perfect-square quadratic. 2. The formula to complete the square for an expression of the form $$x^2 + bx$$ is to add $$\left(\frac{b}{2}\right)^2$$. 3. Here, $$b = -6$$, so we calculate: $$\left(\frac{-6}{2}\right)^2 = (-3)^2 = 9$$ 4. Adding 9 completes the square: $$x^2 - 6x + 9 = (x - 3)^2$$ 5. Therefore, the number that makes the polynomial a perfect-square quadratic is **9**.