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%I #7 Aug 02 2021 08:04:22
%S 8,8,3,3,3,0,1,9,7,1,9,5,8,9,1,9,3,8,9,2,5,8,9,6,4,5,0,8,8,5,6,7,7,1,
%T 0,7,2,3,5,0,5,9,0,0,8,8,4,2,3,1,8,8,2,3,1,6,6,7,6,3,6,6,7,3,1,6,3,4,
%U 3,1,9,5,8,7,3,3,2,2,6,1,2,9,9,8,7,3,3,1,6,8,8,3,1,9,8,3,3,3,1
%N Decimal expansion of x < 0 satisfying 2*x^2+x*cos(x) = 1.
%C See A199170 for a guide to related sequences. The Mathematica program includes a graph.
%e negative: -0.883330197195891938925896450885677107...
%e positive: 0.522945946113111737247623836359811237...
%t a = 2; b = 1; c = 1;
%t f[x_] := a*x^2 + b*x*Cos[x]; g[x_] := c
%t Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t r = x /. FindRoot[f[x] == g[x], {x, -.84, -.83}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199188 *)
%t r = x /. FindRoot[f[x] == g[x], {x, .52, .53}, WorkingPrecision -> 110]
%t RealDigits[r] (* A199189 *)
%Y Cf. A199170.
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Nov 04 2011
%E Offset corrected by _Georg Fischer_, Aug 02 2021