Quadratic Equation Abd8Cd

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 by factoring, completing the square, or 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. **Try factoring:** Notice that $$x^2+4x+4$$ is a perfect square trinomial because $$4x=2\times x \times 2$$ and $$4=2^2$$. 5. **Factor the quadratic:** $$x^2+4x+4 = (x+2)^2$$. 6. **Set the factor equal to zero:** $$(x+2)^2=0$$. 7. **Solve for $$x$$:** $$x+2=0 \implies x=-2$$. 8. **Final answer:** The equation has one real root, $$x=-2$$, which is a repeated root.