Quadratic Equation 182E92

1. **State the problem:** Solve the quadratic equation $$x^2 + 4x + 4 = 0$$. 2. **Recall the formula:** The quadratic equation $$ax^2 + bx + c = 0$$ can be solved using the quadratic formula $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$. 3. **Identify coefficients:** Here, $$a=1$$, $$b=4$$, and $$c=4$$. 4. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 4^2 - 4 \times 1 \times 4 = 16 - 16 = 0$$. 5. **Since $$\Delta = 0$$, there is one real repeated root:** $$x = \frac{-b}{2a} = \frac{-4}{2 \times 1} = \frac{-4}{2}$$. 6. **Simplify the fraction:** $$x = \frac{\cancel{ -4 }}{\cancel{ 2 }} = -2$$. 7. **Final answer:** The solution to the equation is $$x = -2$$.