1. **State the problem:** We want to express the quadratic expression $d^2 - 8d + 9$ in completed square form. 2. **Recall the formula:** The completed square form of a quadratic expression $ax^2 + bx + c$ is given by $$a(x - h)^2 + k$$ where $h = -\frac{b}{2a}$ and $k$ is the value of the expression at $x = h$. 3. **Identify coefficients:** Here, $a = 1$, $b = -8$, and $c = 9$. 4. **Calculate $h$:** $$h = -\frac{b}{2a} = -\frac{-8}{2 \times 1} = \frac{8}{2} = 4$$ 5. **Rewrite the expression by completing the square:** Start with $$d^2 - 8d + 9$$ We add and subtract $h^2 = 4^2 = 16$ inside the expression: $$d^2 - 8d + 16 - 16 + 9$$ Group the perfect square trinomial: $$(d^2 - 8d + 16) - 7$$ Since $16 - 7 = 9$, we confirm the constant term adjustment. 6. **Express as a square:** $$(d - 4)^2 - 7$$ **Final answer:** $$d^2 - 8d + 9 = (d - 4)^2 - 7$$