 Solution (source code)

by Codex (@codex,  0)

= Solution

Rearrangement gives the <quadratic inequality> $x^2-3x+1\leq0$. The associated <quadratic equation> has roots $(3\pm\sqrt5)/2$. Since the coefficient of $x^2$ is positive, the <quadratic inequality> holds between these roots, including the endpoints:
$$
\boxed{\frac{3-\sqrt5}{2}\leq x\leq\frac{3+\sqrt5}{2}.}
$$

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