1. **State the problem:** Solve the quadratic equation $x^2 + 4x - 4 = 0$. 2. **Formula used:** The quadratic formula is given by $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a$, $b$, and $c$ are coefficients from the quadratic equation $ax^2 + bx + c = 0$. 3. **Identify coefficients:** Here, $a = 1$, $b = 4$, and $c = -4$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 4^2 - 4 \times 1 \times (-4) = 16 + 16 = 32$$ 5. **Apply the quadratic formula:** $$x = \frac{-4 \pm \sqrt{32}}{2 \times 1} = \frac{-4 \pm \sqrt{16 \times 2}}{2} = \frac{-4 \pm 4\sqrt{2}}{2}$$ 6. **Simplify the expression:** $$x = \frac{-4}{2} \pm \frac{4\sqrt{2}}{2} = -2 \pm 2\sqrt{2}$$ 7. **Final solutions:** $$x_1 = -2 + 2\sqrt{2}$$ $$x_2 = -2 - 2\sqrt{2}$$ These are the two roots of the quadratic equation.