Can anyone isolate "x" in this expression? 1 = 4cx^2y^3/a^3-3cy/a+c/x

[littlepig]

1 = 4cx^2y^3/a^3-3cy/a+c/x

My math skills have deteriorated over the years and I don't know just what to do with this equation to end up with an x = ..... Can anyone help?

littlepig

 

[HallsofIvy]

After you multiply both sides by x, that is a "reduced" cubic equation of the form \(\displaystyle \alpha x^3+ \gamma x+ \delta= 0\) ("reduced" because there is no square term) with \(\displaystyle \alpha= \frac{4cy^3}{a^3}\), \(\displaystyle \gamma= -(\frac{3cy}{a}+ 1)\), and \(\displaystyle \delta= c\). It can be solved useing Cardano's cubic formula, http://www.math.vanderbilt.edu/~schectex/courses/cubic/, but it is much more complicated than the quadratic formula.

 

[Deleted member 4993]

1 = 4cx^2y^3/a^3-3cy/a+c/x

My math skills have deteriorated over the years and I don't know just what to do with this equation to end up with an x = ..... Can anyone help?

littlepig

You cannot isolate 'x' in that equation (neither can I).

One more thing - you have 'y' in the equation.

Exactly what do you want to do with this equation (other than isolating 'x'). What is your final objective?

Depending on that, we can suggest different numerical schemes.

 

[mmm4444bot]

1 = 4cx^2y^3/a^3-3cy/a+c/x

Texting rational math-expressions without using any grouping symbols often leads to ambiguity.

Without grouping symbols, your typing above represents the following equation. Is this what you intend for us to "see"? :cool:


\(\displaystyle 1 = \frac{4cx^2y^3}{a^3} \;-\; \frac{3cy}{a} \;+\; \frac{c}{x}\)

 

[littlepig]

Texting rational math-expressions without using any grouping symbols often leads to ambiguity.

Without grouping symbols, your typing above represents the following equation. Is this what you intend for us to "see"? :cool:


\(\displaystyle 1 = \frac{4cx^2y^3}{a^3} \;-\; \frac{3cy}{a} \;+\; \frac{c}{x}\)

Yes. Following conventional order of operations there is no other option. Sorry for any confusion.
little pig

 

[littlepig]

You cannot isolate 'x' in that equation (neither can I).

One more thing - you have 'y' in the equation.

Exactly what do you want to do with this equation (other than isolating 'x'). What is your final objective?

Depending on that, we can suggest different numerical schemes.

This equation is a simplified version of a formula to predict spring back when bend spring temper metals. The formula in it's original form has material properties and tooling bend radius as inputs, and the result is the bend radius in the material after it springs open. My intention is reverse the formula so that the resulting spring back is the input and the formulas output would be the tooling radius required to achieve that bend. The other variable in the expression represent the material properties or smaller expressions that repeat and do not contain "x". Using "Goal Seeking" in Excel accomplishes the task, yet I was looking for straight mathematical solution. The "y" is just a letter I chose for the variable "Yeild Strength @ 0.2% offset", one of the required material properties. Sorry for any confusion..
littlepig

 

[mmm4444bot]

Following conventional order of operations there is no other option.

You are correct; however, it seems like less than 10% of people posting on these boards understand the convention! I'm glad that you do.

I used mathematical software (Maple V Release 5) to look for a solution; Maple V provides three Complex solutions (two of which contain an imaginary part).

The Real solution appears as a thumbnail below; click it to view the image at full size.

Cheers ~ Mark :cool:

 

[littlepig]

Thank you

You are correct; however, it seems like less than 10% of people posting on these boards understand the convention! I'm glad that you do.

I used mathematical software (Maple V Release 5) to look for a solution; Maple V provides three Complex solutions (two of which contain an imaginary part).

The Real solution appears as a thumbnail below; click it to view the image at full size.

Cheers ~ Mark :cool:

View attachment 2036

Thank you. I'm impressed. And I wish extend thanks to everyone who replied to my posting. I hadn't used this site before and didn't know what to expect.
littlepig