Answer
$a=-3$.
Work Step by Step
The given polynomial is
$\Rightarrow a^2+6a+9=0$
Write the the polynomial as $a^2+2ab+b^2$.
$\Rightarrow a^2+2(a)(3)+3^2=0$.
Use perfect square trinomial pattern
$a^2+2ab+b^2=(a+b)^2$.
We have $a=a$ and $b=3$.
$\Rightarrow (a+3)^2=0$.
Use zero product property.
$\Rightarrow a+3=0$.
Solve for $a$.
$\Rightarrow a=-3$.
Hence, the solution is $a=-3$.
