Final answer:
The quadratic equation x²+4x+4=0 is a perfect square and can be factored as (x+2)². The solution to the equation is x = -2, which is a repeated root.
Step-by-step explanation:
To solve the given quadratic equation x²+4x+4=0, we can use several methods, including factoring, completing the square, or applying the quadratic formula. However, we can quickly observe that the equation is a perfect square. The left side of the equation can be factored as (x+2)², because x²+4x+4 is the expanded form of (x+2) multiplied by itself.
To find the solutions or roots for this quadratic equation, we set the factored form equal to zero:
(x+2)² = 0
Now, taking the square root of both sides, we have:
x+2 = 0
Therefore, the solution is x = -2, which is a repeated root since the quadratic was a perfect square.