1. **State the problem:** Solve the quadratic equation $$x^2 + 8x - 9 = 0 + 9$$ using the completing the square method. 2. **Simplify the equation:** Move all terms to one side: $$x^2 + 8x - 9 - 9 = 0$$ $$x^2 + 8x - 18 = 0$$ 3. **Isolate the quadratic and linear terms:** $$x^2 + 8x = 18$$ 4. **Complete the square:** Take half of the coefficient of $x$, which is $8$, half is $\frac{8}{2} = 4$, then square it: $$4^2 = 16$$ Add and subtract 16 on the left side to keep the equation balanced: $$x^2 + 8x + 16 - 16 = 18$$ 5. **Rewrite as a perfect square:** $$ (x + 4)^2 - 16 = 18$$ 6. **Move the constant term to the right side:** $$ (x + 4)^2 = 18 + 16$$ $$ (x + 4)^2 = 34$$ 7. **Take the square root of both sides:** $$ x + 4 = \pm \sqrt{34}$$ 8. **Solve for $x$:** $$ x = -4 \pm \sqrt{34}$$ **Final answer:** $$ x = -4 + \sqrt{34} \quad \text{or} \quad x = -4 - \sqrt{34}$$