Answer
The trinomial $x^{2}+6x+c$ is a perfect square when $c=9.$
Then $x^{2}+6x+9=(x+3)(x+3)=(x+3)^{2}$
Work Step by Step
$ x^{2}+6x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{6}{2}=3$.
$\qquad$ ...square the result.
$ 3^{2}=9\qquad$ ...substitute $c$ with $9$ in the original expression
$x^{2}+6x+9=(x+3)^{2}$
