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A199071 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=1.

%I A199071 #8 Feb 07 2025 16:44:05
%S A199071 1,4,0,7,1,0,6,6,3,9,7,6,3,0,3,9,9,0,5,9,9,6,1,6,6,8,8,9,0,3,5,9,5,7,
%T A199071 1,2,8,5,0,8,7,2,6,3,1,0,5,4,0,1,0,4,5,4,1,3,6,1,7,6,9,4,2,3,1,7,2,2,
%U A199071 7,3,2,3,1,9,6,9,6,4,2,7,3,6,7,4,7,2,9,1,3,6,5,2,1,3,2,7,1,6,5
%N A199071 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=1.
%C A199071 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199071 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199071 negative: -1.40710663976303990599616688903595712850...
%e A199071 positive:  0.28352555144412274861845117327862135032...
%t A199071 a = 2; b = 3; c = 1;
%t A199071 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199071 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199071 r = x /. FindRoot[f[x] == g[x], {x, -1.5, -1.4}, WorkingPrecision -> 110]
%t A199071 RealDigits[r] (* A199071 *)
%t A199071 r = x /. FindRoot[f[x] == g[x], {x, .28, .29}, WorkingPrecision -> 110]
%t A199071 RealDigits[r] (* A199072 *)
%Y A199071 Cf. A198866.
%K A199071 nonn,cons
%O A199071 1,2
%A A199071 _Clark Kimberling_, Nov 02 2011