Answer
$\left\{-2,-\dfrac{1}{3},\dfrac{1}{3},2\right\}$
Work Step by Step
The given equation, $
9x^4+4=37x^2
,$ is equivalent to
\begin{align*}
9x^4-37x^2+4&=0
.\end{align*}
Using factoring of trinomials, the equation above is equivalent to
\begin{align*}
(x^2-4)(9x^2-1)&=0
.\end{align*}
Equating each factor to zero (Zero Product Property) and solving the variable, then
\begin{array}{l|r}
x^2-4=0 & 9x^2-1=0
\\
x^2=4 & 9x^2=1
\\\\
& x^2=\dfrac{1}{9}
.\end{array}
Taking the square root of both sides (Square Root Property), the equation above is equivalent to
\begin{array}{l|r}
x=\pm\sqrt{4}& x=\pm\sqrt{\dfrac{1}{9}}
\\\\
x=\pm2& x=\pm\dfrac{1}{3}
.\end{array}
Hence, the solution set of the equation $
9x^4+4=37x^2
$ is $\left\{-2,-\dfrac{1}{3},\dfrac{1}{3},2\right\}$.
