Answer
The trinomial $x^{2}+12x+c$ is a perfect square when $c=36.$
Then $x^{2}+12x+36=(x+6)(x+6)=(x+6)^{2}$
Work Step by Step
$ x^{2}+12x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{12}{2}=6$.
$\qquad$ ...square the result.
$ 6^{2}=36\qquad$ ...substitute $c$ with $36$ in the original expression
$x^{2}+12x+36=(x+6)^{2}$
