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A199265 Decimal expansion of x<0 satisfying 2*x^2+x*cos(x)=2.

%I A199265 #9 Feb 07 2025 16:44:05
%S A199265 1,1,1,5,8,6,5,4,7,4,1,7,7,8,0,0,9,2,0,0,2,5,9,0,5,3,5,2,5,3,5,8,5,5,
%T A199265 7,9,2,7,3,6,1,2,8,0,6,6,4,8,7,3,9,7,8,1,7,4,4,6,2,5,9,3,7,6,5,1,2,5,
%U A199265 1,1,5,6,7,6,9,2,4,1,6,1,0,9,0,2,1,6,0,9,2,7,8,4,4,7,0,8,5,6,8
%N A199265 Decimal expansion of x<0 satisfying 2*x^2+x*cos(x)=2.
%C A199265 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199265 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199265 negative: -1.11586547417780092002590535253585579273...
%e A199265 positive:  0.84824964906603356449300167136536010515870...
%t A199265 a = 2; b = 1; c = 2;
%t A199265 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199265 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199265 r = x /. FindRoot[f[x] == g[x], {x, -1.2, -1.1}, WorkingPrecision -> 110]
%t A199265 RealDigits[r]   (* A199265 *)
%t A199265 r = x /. FindRoot[f[x] == g[x], {x, .84, .85}, WorkingPrecision -> 110]
%t A199265 RealDigits[r]   (* A199266 *)
%Y A199265 Cf. A199170.
%K A199265 nonn,cons
%O A199265 1,4
%A A199265 _Clark Kimberling_, Nov 04 2011