Solve for w w^2+4w+4=0

$w^{2} + 4 w + 4 = 0$

Factor using the perfect square rule.

Rewrite $4$ as $2^{2}$ .

$w^{2} + 4 w + 2^{2} = 0$

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$4 w = 2 \cdot w \cdot 2$

Rewrite the polynomial.

$w^{2} + 2 \cdot w \cdot 2 + 2^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = w$ and $b = 2$ .

${(w + 2)}^{2} = 0$

Set the $w + 2$ equal to $0$ .

$w + 2 = 0$

Subtract $2$ from both sides of the equation.

$w = - 2$