Answer
7
Work Step by Step
Set the $RHS$ to 0 by subtracting $14m$ and adding 49 to both sides:
$m^{2}=14m-49 \qquad.../-14m+49$
$m^{2}-14m+49=0$
In R-2, see "Perfect square" in Special Factorizations.
$(A+B)^{2}=A^{2}+2AB+B^{2}$
$(A-B)^{2}=A^{2}-2AB+B^{2}$
$m^{2}$ is the square of m,
49 is the square of 7, and
14m = 2(m)(7).
Our equation becomes
$(m-7)^{2}=0$
which can only be if
$ m-7=0,\qquad$ so
$m=7$
