1. **State the problem:** Solve the quadratic equation $x^2 + 4x = 5$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 + 4x - 5 = 0$$ 3. **Identify coefficients:** Here, $a=1$, $b=4$, and $c=-5$. 4. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ 5. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 4^2 - 4 \times 1 \times (-5) = 16 + 20 = 36$$ 6. **Find the square root of the discriminant:** $$\sqrt{36} = 6$$ 7. **Calculate the two solutions:** $$x_1 = \frac{-4 + 6}{2} = \frac{2}{2} = 1$$ $$x_2 = \frac{-4 - 6}{2} = \frac{-10}{2} = -5$$ 8. **Final answer:** The solutions to the equation are $x=1$ and $x=-5$.