Why do I get one extra wrong solution when solving 2−x=−√x2-x=-\sqrt{x}?

I’m trying to solve this equation:
2x=x
Multiply by (1):
x=x2
power of 2:
x=(x2)2
then:
x25x+4=0
and that means:
x=1,x=4


But x=1 is not a correct solution to the original equation.

Why have I got it? I’ve never got a wrong solution to an equation before. What is so special here?

Answer

This is because the equation x=x2 is not equivalent to x=(x2)2, but to
x=(x2)2andx2.
Remember x, when it is defined, denotes the non-negative square root of x, hence in the present case, x20, i.e. x must be at least 2.

Attribution
Source : Link , Question Author : TheLogicGuy , Answer Author : Bernard

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