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A199273 Decimal expansion of x<0 satisfying 2*x^2+3*x*cos(x)=1.

%I A199273 #8 Feb 07 2025 16:44:05
%S A199273 1,1,1,2,7,0,7,1,6,1,2,2,3,2,1,9,3,9,2,1,0,5,2,6,0,4,3,8,8,8,3,5,1,3,
%T A199273 3,0,9,1,0,3,3,7,9,6,2,3,1,2,5,2,5,1,2,7,4,0,7,4,6,5,6,5,6,5,3,3,4,2,
%U A199273 3,4,6,5,8,4,2,7,1,2,8,1,2,2,5,3,6,9,0,4,5,1,5,0,4,0,8,9,7,2,1
%N A199273 Decimal expansion of x<0 satisfying 2*x^2+3*x*cos(x)=1.
%C A199273 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199273 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199273 negative: -1.11270716122321939210526043888351330910...
%e A199273 positive:  0.289505448385867415592179483198982452381...
%t A199273 a = 2; b = 3; c = 1;
%t A199273 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199273 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199273 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199273 RealDigits[r]    (* A199273 *)
%t A199273 r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
%t A199273 RealDigits[r]    (* A199274 *)
%Y A199273 Cf. A199170.
%K A199273 nonn,cons
%O A199273 1,4
%A A199273 _Clark Kimberling_, Nov 04 2011