#include <iostream.h>
#include <math.h>

void main()
{
	double x,x1,x2, fx, df, dx, root;
	int j;
//  guess for the range  
	x1 = 1.0; x2 = 4.0 ;
	x = 0.5*(x1+x2);    // first guess =  midpoint of the interval [x1,x2]  
	for (j=1;j<=100; j++)
	{
		fx = x*x - x -1.0;  //  f(x) = x^2-x-1 
		df = 2*x - 1.0;         //  f'(x) = 2x 
		dx = -fx/df;
		x += dx;
		cout<<x<<"\t"<<fx<<endl;
		if (fabs(dx) < 1e-10)
		{
			root=x;		
			break;
		}
	}
	cout<<"found root after "<<j<<" guess : "<<root<<endl;
}