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A199293 Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 2.

%I A199293 #13 Feb 07 2025 16:44:05
%S A199293 1,0,8,3,5,1,1,6,6,1,0,2,1,9,2,8,9,8,8,3,3,0,4,7,4,9,1,0,3,8,2,1,2,5,
%T A199293 5,8,3,1,2,5,4,1,8,9,2,0,1,6,8,0,8,4,8,2,7,8,3,4,5,3,7,5,8,7,4,4,4,2,
%U A199293 9,2,4,6,1,7,9,3,3,4,3,9,2,9,5,4,0,9,0,6,8,8,0,8,7,7,9,4,1,7,3,6,6
%N A199293 Decimal expansion of x < 0 satisfying 3*x^2 + 3*x*cos(x) = 2.
%C A199293 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199293 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199293 negative: -1.0835116610219289883304749103821255...
%e A199293 positive:  0.48645750461686637457544128449375285...
%t A199293 a = 3; b = 3; c = 2;
%t A199293 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199293 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199293 r = x /. FindRoot[f[x] == g[x], {x, -1, -.9}, WorkingPrecision -> 110]
%t A199293 RealDigits[r]    (* A199293 *)
%t A199293 r = x /. FindRoot[f[x] == g[x], {x, .48, .49}, WorkingPrecision -> 110]
%t A199293 RealDigits[r]    (* A199294 *)
%Y A199293 Cf. A199170, A199294.
%K A199293 nonn,cons
%O A199293 1,3
%A A199293 _Clark Kimberling_, Nov 05 2011
%E A199293 a(90) onwards corrected by _Georg Fischer_, Aug 03 2021