1. **State the problem:** Solve the quadratic equation $$x^2 - 3x - 2 = 0$$ by factorization or formula. 2. **Recall the quadratic equation:** The general form is $$ax^2 + bx + c = 0$$ and the solutions can be found by factorization or the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Rewrite the equation:** $$x^2 - 3x - 2 = 0$$. 4. **Try factorization:** Find two numbers that multiply to $$-2$$ and add to $$-3$$. These are $$-1$$ and $$-2$$. 5. **Factor the quadratic:** $$x^2 - 3x - 2 = x^2 - x - 2x - 2 = x(x - 1) - 2(x - 1) = (x - 1)(x - 2) = 0$$. 6. **Set each factor to zero:** $$x - 1 = 0 \Rightarrow x = 1$$ $$x - 2 = 0 \Rightarrow x = 2$$ 7. **Final answer:** The solutions are $$x = 1$$ or $$x = 2$$. This completes the solution by factorization.