HMMT 2006 U7

Find all real numbers $x$ such that

$x^{2}+\left\lfloor\frac{x}{2}\right\rfloor+\left\lfloor\frac{x}{3}\right\rfloor=10$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

-\sqrt{14}

Solutions

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