Thread: Finding x when x has different indices. How do I simplify, please?

12x^6 + 7x^4 = 9315

Forgive my inadequacies, but could somebody show the steps I need to make x the subject?
I don't know how to do this when x doesn't have the same power index.
Any help appreciated. Thanks.

Hey TheDunce.

You will have to transform this into a cubic using the transformation u = x^2 to get 12u^3 + 7u^2 - 9315 = 0 and then use the cubic formula to solve for u first and then x using the relation between x and u.

Cubic function - Wikipedia, the free encyclopedia

Here's some information about the Cubic Formula.

Hello, TheDunce!

I don't know how to do this when x doesn't have the same power index. ??

Does this mean that you have never ever solved a quadratic equation?
Then who assigned you a sixth-degree equaton?


We have: .

We find that are roots of the equation

. . and that: .

The quartic has no real roots.

Therefore, the only real roots are: .

Thanks for the quick replies. I will study this. I'm trying to learn from a textbook and didn't know where to start on this one.
Soroban: I've solved some quadratic equations and used the quadratic formula so I guess the comment didn't make sense. Thanks for the help.