1. **State the problem:** Solve the quadratic equation $$x^2 + 18x + 62 = 0$$ by completing the square. 2. **Recall the formula and rule:** To complete the square for an equation of the form $$x^2 + bx + c = 0$$, we rewrite it as $$\left(x + \frac{b}{2}\right)^2 = \text{some number}$$ by adding and subtracting $$\left(\frac{b}{2}\right)^2$$. 3. **Rewrite the equation:** $$x^2 + 18x + 62 = 0$$ Move the constant term to the right side: $$x^2 + 18x = -62$$ 4. **Complete the square:** Calculate $$\left(\frac{18}{2}\right)^2 = 9^2 = 81$$. Add and subtract 81 on the left side: $$x^2 + 18x + 81 - 81 = -62$$ Group the perfect square trinomial: $$\left(x + 9\right)^2 - 81 = -62$$ 5. **Isolate the perfect square:** $$\left(x + 9\right)^2 = -62 + 81$$ $$\left(x + 9\right)^2 = 19$$ 6. **Solve for x:** Take the square root of both sides: $$x + 9 = \pm \sqrt{19}$$ 7. **Isolate x:** $$x = -9 \pm \sqrt{19}$$ **Final answer:** $$x = -9 + \sqrt{19} \quad \text{or} \quad x = -9 - \sqrt{19}$$