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A199176 Decimal expansion of x<0 satisfying x^2+2*x*cos(x)=1.

%I A199176 #8 Feb 07 2025 16:44:05
%S A199176 1,3,0,1,2,0,1,7,3,3,1,4,1,9,1,1,4,0,0,7,9,8,3,9,7,3,6,4,4,4,0,2,6,4,
%T A199176 5,2,2,1,9,1,3,0,0,6,5,7,4,3,0,3,0,4,8,9,2,6,9,4,6,0,5,7,9,4,6,6,0,3,
%U A199176 7,1,9,0,5,4,5,5,9,6,8,1,3,3,2,4,3,2,9,6,9,4,8,2,3,0,7,2,9,2,9
%N A199176 Decimal expansion of x<0 satisfying x^2+2*x*cos(x)=1.
%C A199176 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199176 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199176 negative: -1.301201733141911400798397364440264522...
%e A199176 positive:  0.444416809391791633213083601823107078...
%t A199176 a = 1; b = 2; c = 1;
%t A199176 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199176 Plot[{f[x], g[x]}, {x, -2 Pi, 2 Pi}, {AxesOrigin -> {0, 0}}]
%t A199176 r = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]
%t A199176 RealDigits[r]  (* A199176 *)
%t A199176 r = x /. FindRoot[f[x] == g[x], {x, .44, .45}, WorkingPrecision -> 110]
%t A199176 RealDigits[r]  (* A199177 *)
%Y A199176 Cf. A199170.
%K A199176 nonn,cons
%O A199176 1,2
%A A199176 _Clark Kimberling_, Nov 04 2011