Answer
$m=-10.12,-1.88$
Work Step by Step
$m^2+12m+19=0$
or, $m^2+12m=-19$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=12$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(12)^2}{4}=36$
To complete the square, add $4$ on both sides.
$m^2+12m+36=-19+36$
$\implies (m+6)^2=17$
$\implies m+6=4.12$
and
$\implies m+6=-4.12$
or, $m=-10.12,-1.88$
