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A199078 Decimal expansion of x<0 satisfying 3*x^2+sin(x)=2.

%I A199078 #8 Feb 07 2025 16:44:05
%S A199078 9,7,0,4,1,5,8,4,1,6,3,5,5,9,0,4,4,7,8,4,3,5,9,2,6,5,7,4,3,0,8,4,4,1,
%T A199078 0,3,4,5,4,9,4,2,7,9,9,4,0,0,0,3,2,1,3,3,6,7,2,4,8,1,7,1,3,3,1,9,1,9,
%U A199078 8,1,9,3,6,7,1,2,3,6,1,7,1,0,9,3,6,6,9,8,9,9,0,3,2,9,1,8,3,6,8
%N A199078 Decimal expansion of x<0 satisfying 3*x^2+sin(x)=2.
%C A199078 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199078 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199078 negative: -0.97041584163559044784359265743084410...
%e A199078 positive:  0.676701594073077874194855720384016697...
%t A199078 a = 3; b = 1; c = 2;
%t A199078 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199078 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199078 r = x /.
%t A199078   FindRoot[f[x] == g[x], {x, -.98, -.97}, WorkingPrecision -> 110]
%t A199078 RealDigits[r]   (* A199078 *)
%t A199078 r = x /. FindRoot[f[x] == g[x], {x, .67, .68}, WorkingPrecision -> 110]
%t A199078 RealDigits[r]   (* A199079 *)
%Y A199078 Cf. A198866.
%K A199078 nonn,cons
%O A199078 0,1
%A A199078 _Clark Kimberling_, Nov 03 2011