Final answer:
The equation x^2 + 4x + 4 = 0 is a perfect square and can be factored as (x + 2)^2, which has a root of x = -2.
Step-by-step explanation:
To factorize the equation x² + 4x + 4 = 0, we need to find two numbers that multiply to give 4 and add up to give 4.
In this case, the numbers are 2 and 2.
So the equation can be factored as (x + 2)(x + 2) = 0.
Since both terms are the same, we can write it as (x + 2)² = 0.
To solve for x, we take the square root of both sides, giving us x + 2 = 0.
Solving for x, we get x = -2.