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A199160 Decimal expansion of x<0 satisfying 3*x^2+3*sin(x)=2.

%I A199160 #8 Feb 07 2025 16:44:05
%S A199160 1,2,7,3,9,4,1,9,1,9,4,1,1,5,8,3,3,2,7,0,3,4,0,8,4,7,4,3,4,2,0,5,5,6,
%T A199160 4,3,5,0,6,1,2,3,1,9,6,7,6,0,7,9,9,5,6,6,7,9,1,1,7,0,7,2,4,3,0,1,8,8,
%U A199160 8,5,2,0,2,7,1,7,7,1,6,1,8,8,7,3,5,7,7,5,9,0,0,0,6,9,7,4,9,2,9
%N A199160 Decimal expansion of x<0 satisfying 3*x^2+3*sin(x)=2.
%C A199160 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199160 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199160 negative: -1.27394191941158332703408474342055643506123...
%e A199160 positive:  0.466106421683196411148081035304500630437462...
%t A199160 a = 3; b = 3; c = 2;
%t A199160 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199160 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199160 r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
%t A199160 RealDigits[r]  (* A199160 *)
%t A199160 r = x /. FindRoot[f[x] == g[x], {x, .46, .47}, WorkingPrecision -> 110]
%t A199160 RealDigits[r]  (* A199161 *)
%Y A199160 Cf. A198866.
%K A199160 nonn,cons
%O A199160 1,2
%A A199160 _Clark Kimberling_, Nov 03 2011