1. **State the problem:** Solve the quadratic equation $$x^2 + 14x + 48 = 0$$ for $x$. 2. **Recall the quadratic formula:** For any quadratic equation $$ax^2 + bx + c = 0$$, the solutions are given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=14$, and $c=48$ in this problem. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 14^2 - 4 \times 1 \times 48 = 196 - 192 = 4$$ Since $\Delta > 0$, there are two real solutions. 4. **Find the solutions:** $$x = \frac{-14 \pm \sqrt{4}}{2 \times 1} = \frac{-14 \pm 2}{2}$$ 5. **Calculate each root:** - Larger solution: $$x = \frac{-14 + 2}{2} = \frac{-12}{2} = -6$$ - Smaller solution: $$x = \frac{-14 - 2}{2} = \frac{-16}{2} = -8$$ 6. **Final answer:** - Box1 (Larger Solution): $-6$ - Box2 (Smaller Solution): $-8$