1. **State the problem:** Solve the quadratic equation $x^2 - 4 = 0$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identity $$a^2 - b^2 = (a - b)(a + b)$$ where $a = x$ and $b = 2$. 3. **Factor the equation:** $$x^2 - 4 = (x - 2)(x + 2) = 0$$ 4. **Set each factor equal to zero:** $$x - 2 = 0 \quad \text{or} \quad x + 2 = 0$$ 5. **Solve each equation:** $$x = 2 \quad \text{or} \quad x = -2$$ 6. **Final answer:** The solutions to the equation $x^2 - 4 = 0$ are $$x = 2 \text{ and } x = -2.$$