Cubic Formula: Step-by-Step Solution for Finding x

Thread starter Strafespar
Start date Mar 25, 2010
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Cubic Formula

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To solve the cubic equation ax^3 + bx^2 + cx + d = 0 for x, one can use the cubic formula, which involves reducing the equation to a depressed cubic form. This is achieved by substituting x with y - b/(3a), simplifying the equation to y^3 + py + q = 0. The next step is to calculate the discriminant to determine the nature of the roots, followed by using Cardano's method to find the roots. The solutions can be expressed in terms of radicals, depending on the discriminant's value. Understanding these steps is crucial for effectively solving cubic equations.

Mar 25, 2010

Strafespar

How would you go about solving ax^3+bx^2+cd+d=0 for x. Please step by step! Thanks!

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Mar 25, 2010

jbunniii

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Strafespar said:

How would you go about solving ax^3+bx^2+cd+d=0 for x. Please step by step! Thanks!

It's pretty longwinded but standard. See here, for example:

http://en.wikipedia.org/wiki/Cubic_function

Mar 25, 2010

Strafespar

In the X_{1} example, does x=y-b/3a?

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