1. **State the problem:** Solve the equation $$(x + 5)^2 - 16 = 0$$ for $x$. 2. **Use the formula:** Recognize this as a difference of squares: $$a^2 - b^2 = (a - b)(a + b)$$ where $$a = x + 5$$ and $$b = 4$$. 3. **Apply the difference of squares:** $$ (x + 5)^2 - 16 = (x + 5 - 4)(x + 5 + 4) = (x + 1)(x + 9) = 0 $$ 4. **Solve each factor:** - Set $$x + 1 = 0$$ which gives $$x = -1$$. - Set $$x + 9 = 0$$ which gives $$x = -9$$. 5. **Check the options:** The solutions are $$x = -1$$ and $$x = -9$$. 6. **Final answer:** The two numbers that solve the equation are **-9** and **-1**.