1. **State the problem:** Solve the quadratic equation $$x^2 + 8x + 15 = 0$$. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a = 1$$, $$b = 8$$, and $$c = 15$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 8^2 - 4 \times 1 \times 15 = 64 - 60 = 4$$. 5. **Find the roots:** $$x = \frac{-8 \pm \sqrt{4}}{2 \times 1} = \frac{-8 \pm 2}{2}$$. 6. **Calculate each solution:** - $$x_1 = \frac{-8 + 2}{2} = \frac{-6}{2} = -3$$ - $$x_2 = \frac{-8 - 2}{2} = \frac{-10}{2} = -5$$ 7. **Final answer:** The solution set is $$\boxed{\{-5, -3\}}$$.