HMMT 2015 U30

Find the sum of squares of all distinct complex numbers $x$ satisfying the equation

$0=4 x^{10}-7 x^{9}+5 x^{8}-8 x^{7}+12 x^{6}-12 x^{5}+12 x^{4}-8 x^{3}+5 x^{2}-7 x+4$

Dataset text NuminaMath olympiads. Quoted with source.

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-\frac{7}{16}

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