1. **State the problem:** Solve the quadratic equation $$x^2 + 2x - 80 = 0$$ by factoring. 2. **Recall the factoring method:** To factor a quadratic equation of the form $$ax^2 + bx + c = 0$$, we look for two numbers that multiply to $$ac$$ and add to $$b$$. 3. **Apply to our equation:** Here, $$a=1$$, $$b=2$$, and $$c=-80$$. We need two numbers that multiply to $$1 \times (-80) = -80$$ and add to $$2$$. 4. **Find the numbers:** The pair $$10$$ and $$-8$$ works because $$10 \times (-8) = -80$$ and $$10 + (-8) = 2$$. 5. **Rewrite the middle term:** $$x^2 + 10x - 8x - 80 = 0$$ 6. **Group terms:** $$(x^2 + 10x) + (-8x - 80) = 0$$ 7. **Factor each group:** $$x(x + 10) - 8(x + 10) = 0$$ 8. **Factor out the common binomial:** $$(x - 8)(x + 10) = 0$$ 9. **Set each factor equal to zero:** $$x - 8 = 0 \quad \Rightarrow \quad x = 8$$ $$x + 10 = 0 \quad \Rightarrow \quad x = -10$$ **Final answer:** $$x = 8$$ or $$x = -10$$