Solve for q q^2+6q+9=0

$q^{2} + 6 q + 9 = 0$

Step 1

Factor using the perfect square rule.

Rewrite $9$ as $3^{2}$ .

$q^{2} + 6 q + 3^{2} = 0$

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

$6 q = 2 \cdot q \cdot 3$

Rewrite the polynomial.

$q^{2} + 2 \cdot q \cdot 3 + 3^{2} = 0$

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = q$ and $b = 3$ .

${(q + 3)}^{2} = 0$

Step 2

Set the $q + 3$ equal to $0$ .

$q + 3 = 0$

Step 3

Subtract $3$ from both sides of the equation.

$q = - 3$