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A199075 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=3.

%I A199075 #8 Feb 07 2025 16:44:05
%S A199075 1,7,2,6,7,8,5,3,2,2,3,7,1,0,9,3,1,9,6,9,4,1,7,1,4,1,6,8,5,6,3,4,9,9,
%T A199075 4,6,6,1,7,1,0,5,8,0,5,9,3,1,3,0,0,9,9,3,9,4,8,9,0,9,7,0,2,8,1,6,5,7,
%U A199075 4,3,2,2,7,6,5,3,3,0,3,2,0,3,4,8,7,4,2,3,1,7,3,3,6,2,6,1,8,7,9
%N A199075 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=3.
%C A199075 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199075 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199075 negative: -1.72678532237109319694171416856349946617...
%e A199075 positive:  0.71708638918192182669700429533330771873...
%t A199075 a = 2; b = 3; c = 3;
%t A199075 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199075 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199075 r = x /. FindRoot[f[x] == g[x], {x, -1.8, -1.7}, WorkingPrecision -> 110]
%t A199075 RealDigits[r] (* A199075 *)
%t A199075 r = x /. FindRoot[f[x] == g[x], {x, .71, .72}, WorkingPrecision -> 110]
%t A199075 RealDigits[r] (* A199076 *)
%Y A199075 Cf. A198866.
%K A199075 nonn,cons
%O A199075 1,2
%A A199075 _Clark Kimberling_, Nov 03 2011