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I'm tell you to solve the following
2(x-1)=x^2 or 2(x-1)=-x^2

thanks

getting rid of the inequalities made it a lot simpler.

how would you know how to replace the inequalities back into the answer?

analytically, I mean

One of the equations you solve, you will get a complex answer.
The other equation you solve, will give you two real solutions. You should see x=-1+sqrt(3) or x=-1-sqrt(3).
You can test intervals to see where we have 2|x-1|

|dw:1380904086865:dw|
2|-10-1|<10^2 True/False 2|0-1|<0^2 True/False
2|10-1|<10^2 True/False

The inequalities that come back true are the intervals you want to include in your solution.

and I was thrown off by the complex solution too

thanks

Np. Have fun. :)