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A199072 Decimal expansion of x>0 satisfying 2*x^2+3*sin(x)=1.

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