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A199056 Decimal expansion of x<0 satisfying x^2+3*sin(x)=2.

%I A199056 #8 Feb 07 2025 16:44:05
%S A199056 2,1,3,1,0,4,7,7,6,4,0,5,6,3,5,5,7,1,0,0,0,1,1,3,3,6,9,5,3,5,8,5,5,3,
%T A199056 8,8,7,1,6,9,6,5,8,2,1,6,7,7,7,6,2,1,4,8,1,1,0,6,6,9,0,2,9,9,1,0,1,9,
%U A199056 6,2,6,3,2,9,5,7,4,2,0,2,9,4,8,2,7,1,0,7,2,2,7,9,3,3,0,4,9,1,9
%N A199056 Decimal expansion of x<0 satisfying x^2+3*sin(x)=2.
%C A199056 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199056 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199056 negative: -2.131047764056355710001133695358553...
%e A199056 positive:  0.58532056434199307654267468696737728...
%t A199056 a = 1; b = 3; c = 2;
%t A199056 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199056 Plot[{f[x], g[x]}, {x, -3, 2}, {AxesOrigin -> {0, 0}}]
%t A199056 r = x /. FindRoot[f[x] == g[x], {x, -2.2, -2.1}, WorkingPrecision -> 110]
%t A199056 RealDigits[r]    (* A199056 *)
%t A199056 r = x /. FindRoot[f[x] == g[x], {x, .58, .59}, WorkingPrecision -> 110]
%t A199056 RealDigits[r]    (* A199057 *)
%Y A199056 Cf. A198866.
%K A199056 nonn,cons
%O A199056 1,1
%A A199056 _Clark Kimberling_, Nov 02 2011