1. **State the problem:** Solve the equation $a^2 - 49 = 0$ by factoring. 2. **Recall the formula:** This is a difference of squares, which factors as $x^2 - y^2 = (x - y)(x + y)$. 3. **Apply the formula:** Here, $a^2 - 49 = a^2 - 7^2 = (a - 7)(a + 7)$. 4. **Set each factor equal to zero:** \begin{align*} a - 7 &= 0 \\ a + 7 &= 0 \end{align*} 5. **Solve each equation:** \begin{align*} a &= 7 \\ a &= -7 \end{align*} 6. **Final answer:** The solutions are $a = 7$ and $a = -7$.