%I #8 Aug 09 2021 07:34:00

%S 1,3,8,9,4,3,7,4,5,2,7,0,4,8,2,8,3,8,9,2,9,1,4,9,8,2,5,1,4,2,9,1,8,9,

%T 2,5,5,9,6,3,3,7,3,5,7,5,8,4,7,5,0,8,3,7,1,4,1,5,6,7,2,2,7,2,9,3,7,0,

%U 4,8,1,2,4,4,7,1,1,8,9,3,8,8,4,3,6,2,8,7,1,0,6,3,2,6,9,4,2,2,6

%N Decimal expansion of x<0 having x^2+x=3*cos(x).

%C See A197737 for a guide to related sequences. The Mathematica program includes a graph.

%e negative: -1.38943745270482838929149825142918925596337...

%e positive: 0.9297344303618125096887004946976108824038...

%t a = 1; b = 1; c = 3;

%t f[x_] := a*x^2 + b*x; g[x_] := c*Cos[x]

%t Plot[{f[x], g[x]}, {x, -2, 1.5}]

%t r1 = x /. FindRoot[f[x] == g[x], {x, -1.4, -1.3}, WorkingPrecision -> 110]

%t RealDigits[r1] (* A197811 *)

%t r2 = x /. FindRoot[f[x] == g[x], {x, .92, .93}, WorkingPrecision -> 110]

%t RealDigits[r2] (* A197812 *)

%Y Cf. A197737.

%K nonn,cons

%O 1,2

%A _Clark Kimberling_, Oct 20 2011