Answer
Fill the blank with: $9$
Work Step by Step
$x^{2}+6x$ is a part of $\quad$
$ x^{2}+2\cdot x\cdot\fbox{$3$} +\fbox{$3^{2}$}=(x+3)^{2}$
so we add $9$ (that is, $3^{2}$) to both sides
to complete the square on the LHS.
We obtain
$x^{2}+6x+9=7+9$
$(x+3)^{2}=16$,
from which, by the square root property, follows:
$x+3=\pm 4$
$x=-3\pm 4$
Solution set = $\{-7,+1\}$
Fill the blank with: $9$
