SOLUTION: (2x - 1 )2 -4(2x -1)+ 2 =0 Not sure about my solution

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Question 180885: (2x - 1 )2 -4(2x -1)+ 2 =0
Not sure about my solution
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Start with the given equation.

Let (notice there are two terms that contain )

Plug in

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for z

Start with the quadratic formula

Plug in , , and

Negate to get .

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

Break up the fraction.

Reduce.

or Break up the expression.

So the answers (in terms of z) are or

However, we need the solutions in terms of "x". Remember, we let , so...

or Go back to the solutions (in terms of "z")

or Plug in

or Add 1 to both sides (for each equation).

or Combine like terms.

or Divide both sides by 2 (for each equation) to isolate "x".

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Answer:

So the solutions are or