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.

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

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

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

Here's some information about the Cubic Formula.

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

Hello, TheDunce!

Quote:

$\displaystyle \text{Solve: }\:12x^6 + 7x^4 \:=\: 9315$

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: .$\displaystyle 12x^6 + 7x^4 - 9315 \:=\:0$

We find that $\displaystyle x = \pm3$ are roots of the equation

. . and that: .$\displaystyle 12x^6 + 7x^4 - 9315 \;=\;(x^2-9)(12x^4 + 115x^2 + 1035)$

The quartic has no real roots.

Therefore, the only real roots are: .$\displaystyle x \:=\:+3,\,-3$

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

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.