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%I #10 Aug 03 2021 14:26:06
%S 1,4,9,3,5,1,9,2,8,0,8,6,8,8,9,1,0,5,6,5,5,6,3,3,9,5,0,9,9,3,4,7,8,1,
%T 8,2,5,3,5,5,3,8,1,3,0,7,4,1,8,8,4,7,6,4,8,1,6,4,1,8,0,2,9,9,2,7,6,3,
%U 4,0,0,6,0,8,5,8,4,0,4,0,8,6,5,1,5,6,3,5,2,0,3,0,4,0,4,1,8,6,2
%N Decimal expansion of x < 0 satisfying x^2 + 2*x*cos(x) = 2.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -1.49351928086889105655633950993478182...
%e positive: 0.94494832910354696494592764037834555...
%t a = 1; b = 2; c = 2;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -5, 3}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199178 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .2, .53}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199179 *)
%Y Cf. A199170, A199179.
%K nonn,cons
%O 1,2
%A _Clark Kimberling_, Nov 04 2011
%E a(91) onwards corrected by _Georg Fischer_, Aug 03 2021