Answer
$x=-5,-2,2,5$
Work Step by Step
Using the factoring of trinomials, the given equation, $
x^4-29x^2+100=0
,$ is equivalent to
\begin{align*}
(x^2-25)(x^2-4)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving for the variable results to
\begin{align*}
\begin{array}{l|r}
x^2-25=0 & x^2-4=0
\\
x^2-25+25=0+25 & x^2-4+4=0+4
\\
x^2=25 & x^2=4
\end{array}
\end{align*}
Taking the square root of both sides (Square Root Principle), the equations above are equivalent to
\begin{align*}
\begin{array}{l|r}
x=\pm\sqrt{25} & x=\pm\sqrt{4}
\\
x=\pm5 & x=\pm2
\end{array}
\end{align*}
Hence, the solutions to the equation $x^4-29x^2+100=0$ are $x=-5,-2,2,5$.
