Solving a Quadratic Equation with Unknown X Coefficient: Homework Help

[Need-Help]

Homework Statement

Homework Equations

x(2x^2 - 5) = -1

The Attempt at a Solution

This question has been flung at me without any pre-examples how to solve it. I have only dealt with equations like 2x^2 + 5x - 12 = 0. I know that the equation above should be set to zero, but how do I deal with the x coefficient on the paranthesis?

I don't know how to solve this -- it's very confusing and if someone can help me I would be grateful!

 

[Need-Help]

I know I need to factorize which is my problem, I am not sure how to when there is an x outside the paramnthesis?

 

[eumyang]

Well, the first thing is that this is not a quadratic equation. It is a cubic. Second, when solving polynomial equations, I would first remove all parentheses (by using the distributive law or by multiplying out) and then collect all terms to the left side. Only then would I try to factor, if possible.

 

[Need-Help]

Do you think there has been a mistake then because the unit I am on is [specifically] quadratic equations? No wonder I wasn't sure about it... If I multiply it out I get

2x^3 - 5x = -1

and then

2x^3 - 5x + 1 = 0

right?

 

[Need-Help]

So how do I factor that? I've never factored a cubic equation...

 

[eumyang]

Yes, the work is correct. Is this problem from a book? There are three solutions, none of which are rational, so I wonder if there was a typo somewhere.

 

[Need-Help]

It does actually say, make correct to the first decimal place...?

 

[Need-Help]

and yes, problem from a book... odd to find a cubic equation in the quadratic section...

 

[Need-Help]

will you please show me how to solve this?

 

[eumyang]

This is not solvable by factoring. All three roots are irrational, so that means you cannot use the Rational Roots Theorem either. You could just graph it on a graphing calculator and have it find the solutions for you.

There exists a cubic formula, but it is overly complicated to use, and it is not taught AFAIK in courses in elementary/intermediate algebra or precalculus.