<s>[INST] Basic Algebra Help \begin{align}
x^2-2x+1 &= x^2-2x+1\\
(1-x)^2 &= (x-1)^2\\
\sqrt{(1-x)^2} &= \sqrt{(x-1)^2}\\
1-x &= x-1\\
1-x &= -1\cdot(1-x)\\
1 &= -1
\end{align}
I definitely did something wrong.
 [/INST] $a^2 = b^2$ does not mean $a=b$. For example $1^2 = (-1)^2$ but that doesn't mean $1 = -1$. Instead, all you can conclude is that $|a| = |b|$, which means that $a=b$ or $a=-b$. 
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