The substitution of
![\begin{displaymath}
x=w-{p\over 3w}
\end{displaymath}](v_618.gif) |
(1) |
into the standard form Cubic Equation
![\begin{displaymath}
x^3+px=q.
\end{displaymath}](v_619.gif) |
(2) |
The result reduces the cubic to the equation
![\begin{displaymath}
w^3-{p^3\over 27w^3}-q=0,
\end{displaymath}](v_620.gif) |
(3) |
which is easily turned into a Quadratic Equation in
by multiplying through by
to obtain
![\begin{displaymath}
(w^3)^2-q(w^3)-{\textstyle{1\over 27}}p^3=0.
\end{displaymath}](v_622.gif) |
(4) |
See also Cubic Equation,Quadratic Equation
© 1996-9 Eric W. Weisstein
1999-05-26