1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$. 2. **Formula and rules:** This is a difference of squares equation, which can be factored using the identity $$a^2 - b^2 = (a - b)(a + b)$$. 3. **Factor the equation:** $$x^2 - 25 = (x - 5)(x + 5) = 0$$ 4. **Solve for roots:** Set each factor equal to zero: - $$x - 5 = 0 \implies x = 5$$ - $$x + 5 = 0 \implies x = -5$$ 5. **Interpretation:** The solutions are $$x = 5$$ and $$x = -5$$, which are the points where the parabola crosses the x-axis. **Final answer:** $$x = 5$$ or $$x = -5$$.