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%I #10 Aug 03 2021 14:26:34
%S 9,4,4,9,4,8,3,2,9,1,0,3,5,4,6,9,6,4,9,4,5,9,2,7,6,4,0,3,7,8,3,4,5,5,
%T 5,1,6,8,6,9,7,2,5,6,5,9,9,0,0,8,1,1,2,3,4,6,4,8,9,1,2,1,6,0,6,7,5,6,
%U 5,8,7,8,0,9,6,7,9,2,3,2,9,0,3,1,2,8,2,8,4,2,8,9,8,9,7,8,9,9,6
%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: -1.493519280868891056556339509934781825...
%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, A199178.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 04 2011
%E a(95) onwards corrected by _Georg Fischer_, Aug 03 2021