eq1 := 858.7006*k = 2*g1+858.7006;
eq2 := 4*(w^2+196230) = g1^2+858.7006*g1+g2^2+7840.4*g3+190.4542*w*g4+w^2+196230;
eq3 := 8*(550.1649*w^2+5268000) = 7840.4*g1*g3+190.4542*g1*g4*w+2*g1*w^2+12702*g1-190.4542*g3*g2*w+7840.4*g4*g2-308.5357*g2*w-190.4542*g3*w^2
+3
251900*g3+90661*w*g4+550.1649*w^2+5268000;
eq4 := 16*(72269*w^2+29791000) = g1^2*w^2-190.4542*g1*g3*w^2+7840.4*g1*g4*w+550.1649*g1*w^2+g2^2*w^2-7840.4*g3*g2*w-190.4542*g4*g2*w^2-12702*g2*w+8730.4*g3^2*w^2+11351000*g3^2-54534*g3*w^2+36779000*g3+8730.4*g4^2*w^2+11351000*g4^2+3251900*w*g4+72269*w^2+29791000

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