Equality might be too hard

Algebra Level 5

\[x^2+7x+14+2(x+1)\sqrt{2x+5}+2(2x+3)\sqrt{x+3} \\ +4\sqrt{2x^2+11x+15}=0\] Let the sum of all \(x\) satisfy the equation is \(A\). Find \(10000A\) round to the nearest integer.

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