Another 5000 Follower Problem

Algebra Level 3

P(x)=(x2+5000x1)2+(2x+5000)2P(x)=(x^2+5000x-1)^2+(2x+5000)^2

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

Image Credit: Wikimedia Five Thousand
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