Answer
$x=\{ \pm5,\pm2i\}$
Work Step by Step
Using factoring and then equating each factor to $0$, the solutions of the given quadratic equation, $
x^4-21x^2-100=0
,$ are
\begin{array}{l}\require{cancel}
(x^2-25)(x^2+4)=0
\\\\
x^2-25=0
\\\\
x^2=25
\\\\
x=\pm\sqrt{25}
\\\\
x=\pm5
,\\\\\text{OR}\\\\
x^2+4=0
\\\\
x^2=-4
\\\\
x=\pm\sqrt{-4}
\\\\
x=\pm\sqrt{-1}\cdot\sqrt{4}
\\\\
x=\pm i\cdot2
\\\\
x=\pm 2i
.\end{array}
Hence, $
x=\{ \pm5,\pm2i\}
$.
