1. Stating the problem: Solve the quadratic equation $x^2 + 4x + 4 = 0$.\n\n2. Recognize this is a quadratic equation in standard form $ax^2 + bx + c = 0$ where $a=1$, $b=4$, and $c=4$.\n\n3. Check if the quadratic can be factored. Notice $4 = 2^2$ and $4x = 2 imes 2 imes x$, so this factors as a perfect square:\n$$x^2 + 4x + 4 = (x + 2)^2.$$\n\n4. Set the factor equal to zero and solve for $x$:\n$$(x + 2)^2 = 0 \implies x + 2 = 0 \implies x = -2.$$\n\n5. Therefore, the solution to the equation is $x = -2$. This is a repeated root because the quadratic has a perfect square factor.