function x = p31_sol ( )

%*****************************************************************************80
%
%% p31_sol() returns an approximate minimizer for test 31.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    23 February 2026
%
%  Author:
%
%    John Burkardt
%
%  Output:
%
%    real x: an approximate minimizer.
%
  x = 1.776528787613;

  return
end
