How Do You Solve for t in a Cubic Parametric Equation?

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SUMMARY

The discussion focuses on solving for the variable t in the cubic parametric equation x = at^3 + bt^2 + ct + d. The user expresses difficulty in isolating t and seeks clarification on the complexity of cubic equations compared to quadratic equations. A reference to the general method for expressing the roots of cubic equations is provided, highlighting that it is significantly more complex than the quadratic formula. The coefficients a, b, c, and d are confirmed to be single real number values.

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Homework Statement



Here's the equation:

slove for t

x=at^3+bt^2+ct+d

Homework Equations



Parametic Equations, removing the t value and such, to "simplify" the equation.

The Attempt at a Solution



This is as far as I got:

(x-d)/t = t^2(a+(b/t)+(c/t^2))

I'm stumped. Is this even possible?

Thanks
 
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There is a general method of expressing the roots of a cubic equation in terms of its coefficients, but it is far more complicated than the quadratic formula. You can find it here: http://en.wikipedia.org/wiki/Cubic_function

Are there any constraints on a, b, c, and d?
 
Thanks, yea that looks pretty crazy, but interesting. I had a feeling it was headed that way, I wasn't aware of the cubic function. a,b,c,and d are basically a single real number value, if that's what you mean.

Thanks!
 

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