1. **State the problem:** Solve the quadratic equation $x^2 + 18x - 360 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$. 3. **Identify coefficients:** Here, $a = 1$, $b = 18$, and $c = -360$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 18^2 - 4 \times 1 \times (-360) = 324 + 1440 = 1764$$. 5. **Find the square root of the discriminant:** $$\sqrt{1764} = 42$$. 6. **Apply the quadratic formula:** $$x = \frac{-18 \pm 42}{2 \times 1} = \frac{-18 \pm 42}{2}$$. 7. **Calculate the two solutions:** - For the plus sign: $$x = \frac{-18 + 42}{2} = \frac{24}{2} = 12$$. - For the minus sign: $$x = \frac{-18 - 42}{2} = \frac{-60}{2} = -30$$. 8. **Final answer:** The solutions to the equation are $$x = 12$$ and $$x = -30$$.