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A199154 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=2.

%I A199154 #8 Feb 07 2025 16:44:05
%S A199154 1,1,2,6,2,9,9,9,4,0,9,9,3,8,7,7,5,2,3,9,9,2,8,6,7,7,3,3,6,4,1,8,6,8,
%T A199154 5,0,7,2,2,2,7,0,7,8,8,7,1,8,7,3,6,9,6,8,2,1,0,1,2,4,1,9,8,1,3,2,7,5,
%U A199154 3,6,9,3,2,2,5,1,7,5,0,6,8,2,5,0,4,4,0,7,7,5,3,0,0,7,7,6,0,7,6
%N A199154 Decimal expansion of x<0 satisfying 3*x^2+2*sin(x)=2.
%C A199154 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199154 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199154 negative: -1.126299940993877523992867733641868507222...
%e A199154 positive:  0.559372170813127047765629647326548920708...
%t A199154 a = 3; b = 2; c = 2;
%t A199154 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199154 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199154 r = x /. FindRoot[f[x] == g[x], {x, -1.13, -1.12}, WorkingPrecision -> 110]
%t A199154 RealDigits[r]  (* A199154 *)
%t A199154 r = x /. FindRoot[f[x] == g[x], {x, .55, .56}, WorkingPrecision -> 110]
%t A199154 RealDigits[r]  (* A199155 *)
%Y A199154 Cf. A198866.
%K A199154 nonn,cons
%O A199154 1,3
%A A199154 _Clark Kimberling_, Nov 03 2011