1. **State the problem:** Solve the quadratic equation $$x^2 - 4 = 0$$. 2. **Formula and rules:** To solve a quadratic equation of the form $$ax^2 + bx + c = 0$$, we can use factoring, completing the square, or the quadratic formula. Here, the equation is already simplified and can be factored. 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 for $$x$$:** $$x = 2 \quad \text{or} \quad x = -2$$ 6. **Explanation:** The equation $$x^2 - 4 = 0$$ represents a difference of squares, which factors into $$(x - 2)(x + 2)$$. Setting each factor equal to zero gives the solutions where the parabola crosses the x-axis. **Final answer:** $$x = \pm 2$$