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A199275 Decimal expansion of x<0 satisfying 2*x^2+3*x*cos(x)=2.

%I A199275 #8 Feb 07 2025 16:44:05
%S A199275 1,2,5,7,5,0,7,4,8,2,6,9,6,7,9,7,8,1,2,6,2,4,5,2,2,8,2,0,0,6,8,6,6,9,
%T A199275 2,1,0,2,2,7,8,5,6,0,1,9,8,0,6,8,6,4,9,7,2,4,3,9,0,1,1,4,7,9,5,7,1,4,
%U A199275 7,4,6,4,0,9,9,8,8,2,2,6,4,4,7,6,8,9,8,5,8,2,2,3,6,0,9,1,9,9,1
%N A199275 Decimal expansion of x<0 satisfying 2*x^2+3*x*cos(x)=2.
%C A199275 See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%H A199275 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199275 negative: -1.25750748269679781262452282006866921022...
%e A199275 positive:  0.547005740546889576436923247150755725087...
%t A199275 a = 2; b = 3; c = 2;
%t A199275 f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t A199275 Plot[{f[x], g[x]}, {x, -3, 3}, {AxesOrigin -> {0, 0}}]
%t A199275 r = x /. FindRoot[f[x] == g[x], {x, -1.3, -1.2}, WorkingPrecision -> 110]
%t A199275 RealDigits[r]    (* A199275 *)
%t A199275 r = x /. FindRoot[f[x] == g[x], {x, .54, .55}, WorkingPrecision -> 110]
%t A199275 RealDigits[r]    (* A199276 *)
%Y A199275 Cf. A199170.
%K A199275 nonn,cons
%O A199275 1,2
%A A199275 _Clark Kimberling_, Nov 04 2011