Answer
$x=\pm5$
Work Step by Step
We simplify as follows:
$x^{4}-21x^{2}-100=0$
Let $m=x^{2}$
$m^{2}-21m-100=0$
$(m-25)(m+4)=0$
$m-25=0$ or $m+4=0$
$m=25$ or $m=-4$
$x^{2}=25$ or $x^{2}=-4$
$x=\pm5$
Note that $x^{2}=-4$ has no solution