Question 575965
<font face="Times New Roman" size="+2">


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 36x\ -\ 16x^3\ =\ 9x^2\ -\ 4x^4]


Add *[tex \LARGE -9x^2\ +\ 4x^4] to both sides:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^4\ -\ 9x^2\ -\ 16x^3\ +\ 36x\ =\ 0]


Group and factor out the GCF from each group:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\left(4x^2\ -\ 9\right)\ -\ 4x\left(4x^2\ -\ 9\right)\ =\ 0]


Note that the two quadratic binomials are equal, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x^2\ -\ 4x\right)\left(4x^2\ -\ 9\right)\ =\ 0]


Factor the difference of two squares:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(x^2\ -\ 4x\right)\left(2x\ -\ 3\right)\left(2x\ +\ 3\right)\ =\ 0]


Factor the GCF out of the quadratic binomial:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x\left(x\ -\ 4\right)\left(2x\ -\ 3\right)\left(2x\ +\ 3\right)\ =\ 0]


Finally apply the Zero Product Rule to solve for each of the four expected roots.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<div style="text-align:center"><a href="http://outcampaign.org/" target="_blank"><img src="http://cdn.cloudfiles.mosso.com/c116811/scarlet_A.png" border="0" alt="The Out Campaign: Scarlet Letter of Atheism" width="143" height="122" /></a></div>
</font>