Another 5000 Follower Problem

Algebra Level 3

\[P(x)=(x^2+5000x-1)^2+(2x+5000)^2\]

Let \(P(x)\) be a polynomial, then find the sum of all the real solutions to the equation \[P(x)=\text{min}(P(x)).\]

Image Credit: Wikimedia Five Thousand
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