8-ball

u = [3; 2];
r = 1;
% Expecting x = [3; 0] or roughly x = [1.2; 2.7].

f = @(x) [x'*x+4*r*r-u'*u; x'*x-x'*u];
fp = @(x) [2*x'; 2*x'-u'];
x = [0; 1];

for i=1:10
    x = x - fp(x)\f(x);
    disp(x')
end

#{

This is the output:

octave:3> main
  -0.33333   5.00000
   0.69504   3.45745
   1.0777   2.8835
   1.1509   2.7736
   1.1538   2.7692
   1.1538   2.7692
   1.1538   2.7692
   1.1538   2.7692
   1.1538   2.7692
   1.1538   2.7692

Good! Expected something like [1.2; 2.7].

}#