HMMT 2007 S8

Find the positive real number(s) $x$ such that $\frac{1}{2}\left(3 x^{2}-1\right)=\left(x^{2}-50 x-10\right)\left(x^{2}+25 x+5\right)$ .

Dataset text NuminaMath olympiads. Quoted with source.

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25+2 \sqrt{159}

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