1. Stating 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. Set each factor equal to zero and solve for $x$: $$x - 5 = 0 \implies x = 5$$ $$x + 5 = 0 \implies x = -5$$ 5. Final answer: The solutions to the equation are $x = 5$ and $x = -5$. Since the solutions are integers, surd form is not necessary.