Answer
The solutions are $-3. -1, 1, \text{ and } 3$.
Work Step by Step
The given equation can be written as:
$$(x^2)^2-10x^2+9=0$$
Let $u=x^2$.
Rewrite the equation above using $u$ to obtain:
$$u^2-10u+9=0$$
Factor the trinomial to obtain:
$$(u-9)(u-1)=0$$
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
\\&u-9=0 &\text{or} &u-1=0
\\&u=9 &\text{or} &u=1
\end{array}
Since $u=x^2$, then
\begin{array}{ccc}
\\&u=9 &\text{or} &u=1
\\&x^2=9 &\text{or} &x^2=1
\\&x=\pm\sqrt9 &\text{or} &x=\pm \sqrt1
\\&x=\pm3 &\text{or} &x=\pm 1
\end{array}
Therefore, the solutions are $-3. -1, 1, \text{ and } 3$.
