Is This Equation Solvable: 2*x^2*(x-2)^2 = x+1?

  • Thread starter haiha
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In summary, when faced with a complicated-looking equation, use your knowledge of algebraic manipulations to simplify it. Multiply out brackets, collect like terms, and try to put it into a recognizable form. If there is a mistake in the equation, it may lead to a third order equation, but there are formulas for solving it analytically. However, there is a simple root that can be found by inspection or trying a few numbers. Once this root is found, it can be factored out and the remaining second order polynomial can be solved. This approach can be used for equations that are not necessarily homework problems.
  • #1
haiha
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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.
 
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  • #2
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:
  • #3
You advice still stands - multiply out and factor. Notice that there is a root you can spot from the original form by inspection.
 
  • #4
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.
 
  • #5
Thanks for all the helps. I will try it. Anyway, it is not a homework for sure.
 

FAQ: Is This Equation Solvable: 2*x^2*(x-2)^2 = x+1?

What is the equation "2*x^2*(x-2)^2 = x+1" asking to solve for?

The equation is asking to solve for the value(s) of x that make the statement true.

What is the degree of this equation?

The degree of the equation is 4, since the highest exponent of x is 4.

How many solutions does this equation have?

This equation has four solutions, since it is a fourth-degree polynomial.

What is the best method to solve this equation?

The best method to solve this equation is to simplify it first by expanding and combining like terms, then using the quadratic formula or factoring to find the solutions.

Can this equation have imaginary solutions?

Yes, this equation can have imaginary solutions since it is a fourth-degree polynomial, which can have complex roots.

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