Equation of radicals

Algebra Level 4

Let \(x_0\) be the positive solution to the equation \[\large \frac{\sqrt{1+x^2}}{x} = \sqrt{1+x^2}-1.\] If the expression \( \left((2\sqrt{2}-2)x_0-1\right)^2 \) is of the form \(a+b\sqrt{c}\), where \(a,b,c\) are integers, and \(c\) is square free, what is the value of \(a+b+c\)?

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