Answer
$c=49$
Work Step by Step
The third term of a perfect square trinomial is equal to the square of half of the coefficient of the middle term. Hence, to make the given expression, $
m^2-14m+c
$, a perfect square trinomial, then,
\begin{array}{l}
c=\left( \dfrac{14}{2} \right)^2
\\\\
c=\left( 7 \right)^2
\\\\
c=49
.\end{array}
