$x²+19+8$
$=x²+2.x.\dfrac{19}{2}+\dfrac{361}{4}-\dfrac{329}{4}$
$=(x+\dfrac{19}{2})²-\dfrac{329}{4}$
Vì $(x+\dfrac{19}{2})²≥0$
$→(x+\dfrac{19}{2})²-\dfrac{329}{4}≥-\dfrac{329}{4}$
$→$ Dấu "=" xảy ra khi $x+\dfrac{19}{2}=0$
$↔x=-\dfrac{19}{2}$
$→\min H=-\dfrac{329}{4}$ khi $x=-\dfrac{19}{2}$