Answer
The trinomial $x^{2}+50x+c$ is a perfect square when $c=625.$
Then $x^{2}+50x+625=(x+25)(x+25)=(x+25)^{2}$
Work Step by Step
$ x^{2}+50x+c\qquad$ ... find half the coefficient of $x$, which is $\displaystyle \frac{50}{2}$.
$\qquad$ ...square the result.
$(\displaystyle \frac{50}{2})^{2}=\frac{2500}{4}=625\qquad$ ...substitute $c$ with $625$ in the original expression
$x^{2}+50x+625=(x+25)^{2}$
