1. **State the problem:** Solve the quadratic equation $x^2 + 10x + 13 = 4$ by factoring. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero: $$x^2 + 10x + 13 - 4 = 0$$ $$x^2 + 10x + 9 = 0$$ 3. **Factor the quadratic:** Find two numbers that multiply to $9$ and add to $10$. These numbers are $9$ and $1$. $$x^2 + 9x + x + 9 = 0$$ $$x(x + 9) + 1(x + 9) = 0$$ $$(x + 1)(x + 9) = 0$$ 4. **Solve for $x$:** Set each factor equal to zero: $$x + 1 = 0 \Rightarrow x = -1$$ $$x + 9 = 0 \Rightarrow x = -9$$ 5. **Final answer:** The solutions are $x = -1$ and $x = -9$. This matches the answer choice $x = \{-9, -1\}$ (Answer Two).