Answer
$x=-1$ or $x=-21$
Work Step by Step
We solve by completing the square:
$x^{2}+22x+21=0$
$x^{2}+22x=-21$
$x^{2}+22x+11^{2}=-21+11^{2}=-21+121=100$
$(x+11)^{2}=100$
$x+11=\pm\sqrt{100}=\pm 10$
$x=-11\pm 10$
$x=-11+10=-1$ or $x=-11-10=-21$
So we have: $x=-1$ or $x=-21$