# Physical model for Completing the Cube?

Homework Helper
Gold Member
Completing the Square for finding the general solution for a quadratic equation by using a two dimensional drawing is easy. Since we can not so easily draw a three dimensional figure to help in finding a solution to a cubic equation, has any clever mathematician ever found a three dimensional physical model to help in deriving a solution to a general cubic equation?

I ask because, the method of producing the solution seems to rely on a bunch of new variables without showing clearly how and why it all works. So very different from understanding the quadratic equations.

Mentallic
Homework Helper
Well we can quite easily complete the square not because of how easy it is to model physically but because of the symmetry quadratics have about their axis. Since general cubics don't have this symmetry, I would be very sceptical if any physical interpretations of solving cubics have been found.

Also to complete the cube, mustn't we be able to transform the general cubic into the form $$(x+a)^3+b$$? This cannot be done in general.

epenguin
Homework Helper
Gold Member
Also to complete the cube, mustn't we be able to transform the general cubic into the form $$(x+a)^3+b$$? This cannot be done in general.
The general cubic can be transformed into the form (x + a)3 + (x + b)3