# Solve 2*x^2*(x-2)^2 = x+1

haiha
My friend asks me to solve this one, but i have no idea :

2*x^2*(x-2)^2 = x+1.

Thanks for any hints.

## Answers and Replies

Nancarrow
When you have a complicated-looking equation, you should use whatever knowledge you have of algebraic manipulations, to simplify it.

Multiply out brackets... collect like terms... eventually you'll be able to put it into a form that you recognise.

Also I think your question should go in the homework forums.

ETA: huh, I thought that '*' in the middle of the LHS was a '+'. Your version looks harder! Never mind, try simplifying anyway.

Last edited:
Homework Helper
You advice still stands - multiply out and factor. Notice that there is a root you can spot from the original form by inspection.

lalbatros
If you wrote the equation without mistake: 2*x^2*(x-2)^2 = x+1 ,
then a few simple calculations will lead you to a third order equation, and there are formulas for solving analtically a third order polynimial equation.

However, as matt_grime said, there is one root that is easy to find: just try a few numbers, or make a graphic of the function to guess what is this simple root.

Once you have found this simple root, you can indeed factor it out by division and solve the second order polynomial that still remains.

haiha
Thanks for all the helps. I will try it. Anyway, it is not a homework for sure.