Solving a Cubic Equation: Finding x

NoobixCube · 2008-11-23T22:07:38+00:00

Hey, I have a cubic of this form: \\ax^{3}-bx-c=0\\ how do I solve for x?

Thread starter NoobixCube
Start date Nov 23, 2008
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Cubic

In summary, a cubic equation is an algebraic equation with the highest power of the variable being 3. To solve it, one can use methods such as factoring, the cubic formula, or Cardano's method. The cubic formula is written as x = [-b ± √(b² - 4ac)] / 2a and can be used to find all three solutions for x. However, not all cubic equations have real solutions, as some may have complex or no solutions at all. Solving cubic equations is important in various fields of science and mathematics, as it helps understand and model real-life situations and find optimal solutions to problems.

Nov 23, 2008

NoobixCube

Hey,
I have a cubic of this form:
[tex]\\ax^{3}-bx-c=0\\ [/tex]
how do I solve for [tex]x[/tex]?

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Nov 23, 2008

NoobixCube

It may pay to add that a,b,c are greater than zero...

Nov 23, 2008

HallsofIvy

Science Advisor

Homework Helper

That looks like a reduced cubic to me and for general a, b, c, the solution is given by Cardano's cubic formula:
http://mathworld.wolfram.com/CubicFormula.html

What is a cubic equation?

A cubic equation is a type of algebraic equation in which the highest power of the variable is 3. It can be written in the form ax³ + bx² + cx + d = 0, where a, b, c, and d are constants and x is the variable.

How do you solve a cubic equation?

To solve a cubic equation, you can use different methods such as factoring, the cubic formula, or the Cardano's method. These methods involve manipulating the equation and finding the roots or solutions for x.

What is the cubic formula?

The cubic formula is a method for solving cubic equations. It is written as x = [-b ± √(b² - 4ac)] / 2a, where a, b, and c are the coefficients of the equation. This formula can be used to find all three solutions for x.

Can all cubic equations be solved?

No, not all cubic equations have real solutions. Some cubic equations may have complex solutions, while others may have no solutions at all. It depends on the coefficients of the equation and the nature of the solutions.

Why is it important to solve cubic equations?

Cubic equations are used in various fields of science and mathematics, such as in physics, engineering, and economics. Solving cubic equations can help us understand and model real-life situations, and can also be useful in finding optimal solutions to problems.