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A199073 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=2.

%I A199073 #10 Feb 07 2025 16:44:05
%S A199073 1,5,8,1,1,1,3,5,8,4,2,6,8,0,1,2,6,2,3,6,2,3,5,1,3,3,0,1,1,3,1,8,9,6,
%T A199073 6,7,8,7,2,0,2,3,7,3,1,0,7,9,2,1,8,9,5,8,1,2,5,2,1,2,1,0,4,8,8,9,3,3,
%U A199073 9,5,3,3,2,1,6,1,0,1,2,1,9,4,3,5,4,0,9,3,2,0,7,4,2,5,9,6,1,2,7
%N A199073 Decimal expansion of x<0 satisfying 2*x^2+3*sin(x)=2.
%C A199073 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199073 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199073 negative: -1.5811135842680126236235133011318966...
%e A199073 positive:  0.5132747777025682345171850420249902...
%t A199073 a = 2; b = 3; c = 2;
%t A199073 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199073 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199073 r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
%t A199073 RealDigits[r](* A199073 *)
%t A199073 r = x /. FindRoot[f[x] == g[x], {x, .51, .52}, WorkingPrecision -> 110]
%t A199073 RealDigits[r](* A199074 *)
%o A199073 (PARI) solve(x=1,2, 2*x^2-3*sin(x)-2) \\ _Charles R Greathouse IV_, Dec 06 2016
%Y A199073 Cf. A198866.
%K A199073 nonn,cons
%O A199073 1,2
%A A199073 _Clark Kimberling_, Nov 03 2011