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

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

Step 1

Factor using the perfect square rule.

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

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

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

$4 u = 2 \cdot u \cdot 2$

Rewrite the polynomial.

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

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

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

Step 2

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

$u + 2 = 0$

Step 3

Subtract $2$ from both sides of the equation.

$u = - 2$