clear, clc;

X0=zeros(5,1);
X0(3)=-1+sqrt(1.75);
X0(4)=X0(3);
X0(1)=0.5-X0(3);
X0(2)=1.5-X0(3);
X0(5)=0.09*X0(1)*X0(4)^3/(X0(2)*(sum(X0))^2)

F=@(X) [X(1)+X(3)+X(5)-0.5;
    X(2)+X(3)-X(5)-1.5;
    X(3)-X(4)-3*X(5);
    X(3)*X(4)-1/2*X(1)*X(2);
    X(2)*X(5)*sum(X)^2-0.09*X(1)*X(4)^3];

J=@(X) [1 0 1 0 1;
    0 1 1 0 -1;
    0 0 1 -1 -3;
    -1/2*X(2) -1/2*X(1) X(4) X(3) 0;
    0.09*X(4)^3 X(5)*sum(X)^2 0 -0.09*3*X(1)*X(4)^2 X(2)*sum(X)^2];

delta=inf;

while norm(delta./X0,Inf)>0.5e-4
   delta=J(X0)\F(X0);
   X0=X0-delta;
end
X0
delta