Answer
$c=49$
$(x+7)^{2}$
Work Step by Step
$ x^{2}+14x+c\qquad$ ... find half the coefficient of $x$.
$\displaystyle \frac{14}{2}=7$
$\qquad$ ...square the result.
$ 7^{2}=49\qquad$ ...replace $c$ with $49$ in the original expression
The trinomial $x^{2}+14x+c$ is a perfect square when $c=49.$
Then $x^{2}+14x+49=(x+7)(x+7)=(x+7)^{2}$
