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A199069 Decimal expansion of x<0 satisfying 2*x^2+2*sin(x)=3.

%I A199069 #8 Feb 07 2025 16:44:05
%S A199069 1,5,8,1,1,2,1,9,7,2,2,0,7,4,1,1,9,1,8,3,1,2,8,8,3,1,1,8,0,2,8,2,2,7,
%T A199069 3,5,8,5,0,3,1,0,2,9,7,9,7,6,8,8,0,2,5,6,3,6,4,2,6,9,0,6,4,4,0,3,4,9,
%U A199069 9,2,6,0,8,5,5,3,0,2,1,8,2,3,8,5,5,6,6,5,7,3,9,3,9,0,9,9,8,4,8
%N A199069 Decimal expansion of x<0 satisfying 2*x^2+2*sin(x)=3.
%C A199069 See A198866 for a guide to related sequences. The Mathematica program includes a graph.
%H A199069 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>.
%e A199069 negative: -1.58112197220741191831288311802822735850...
%e A199069 positive:  0.86107767473955299024198236567037763109430...
%t A199069 a = 2; b = 2; c = 3;
%t A199069 f[x_] := a*x^2 + b*Sin[x]; g[x_] := c
%t A199069 Plot[{f[x], g[x]}, {x, -2, 2}, {AxesOrigin -> {0, 0}}]
%t A199069 r = x /. FindRoot[f[x] == g[x], {x, -1.6, -1.5}, WorkingPrecision -> 110]
%t A199069 RealDigits[r](* A199069 *)
%t A199069 r = x /. FindRoot[f[x] == g[x], {x, .86, .87}, WorkingPrecision -> 110]
%t A199069 RealDigits[r] (* A199070 *)
%Y A199069 Cf. A198866.
%K A199069 nonn,cons
%O A199069 1,2
%A A199069 _Clark Kimberling_, Nov 02 2011