Solve the Quadratic Equation: X²+4X+4=0 Step-by-Step

Solve for X:

$X^2+4X+4=0$

To solve the quadratic equation $X^2 + 4X + 4 = 0$, we can attempt to factor it as a perfect square trinomial.

• Step 1: Recognize that the equation is a perfect square trinomial because it can be written as $(X + 2)^2$. The relationship is $(X + 2)(X + 2) = X^2 + 4X + 4$.
• Step 2: Set the factored equation equal to zero: $(X + 2)^2 = 0$.
• Step 3: Solve for $X$ by setting $X + 2 = 0$.
• Step 4: Solving $X + 2 = 0$ gives $X = -2$.

Therefore, the solution to the equation is $X = -2$.

Thus, the correct answer choice is $x = -2$, corresponding to choice 1.