# Can't Factor This Fractional Part

Algebra Level 5

Let $$x$$ be the smallest positive real satisfying $\{x^2\}-2\{x\}+1=0$

Find the value of $\lfloor 1000\{x\}\rfloor$

Details and Assumptions

$$\{n\}$$ is the fractional part of $$n$$. That is, $$\{n\}=n-\lfloor n\rfloor$$ for all positive real $$n$$.

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