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

using namespace std;

double f(double x){
	return (6435.0*pow(x,8)-12012.0*pow(x,6)+6930.0*pow(x,4)-1260.0*pow(x,2)+35)/128.0;
	//return x*x-2.0*x-2.0;
}

double fp(double x){
	return (6435.0*8.0*pow(x,7)-12012.0*6.0*pow(x,5)+6930.0*4.0*pow(x,3)-1260.0*2.0*x)/128.0;
	//return 2.0*x-2.0;
}

int main(int argc, char** argv) {
	double xOld,xNew,xL,xR;
	double Tol,Error,LT,RT;
	int i;
	
	cout<<"Enter xL:"<<endl;
	cin>>xL;
	xOld=xL;
	cout<<"Enter xR:"<<endl;
	cin>>xR;
	cout<<"Enter Tolerance:"<<endl;
	cin>>Tol; 
	
	i=0;
	do{
		LT=(xOld-xL)*fp(xOld)-f(xOld);
		RT=(xOld-xR)*fp(xOld)-f(xOld);
		i++;
		
		if((LT*RT)<0.0){ //We do Newton-Raphson
			xNew=xOld-(f(xOld)/fp(xOld));
			cout<<"Newton-Raphson i= "<<i<<" xNew= "<<xNew<<endl;
		}
		else{ //We do Bisection
			xNew=(xR+xL)/2.0;
			cout<<"Bisection i= "<<i<<" xNew= "<<xNew<<endl;
		}
		
		//Change xR or xL
		if((f(xL)*f(xNew))<0.0){ //Root is between xL and xNew
			xR=xNew;
		}
		else{ //Root is between xNew and xR
			xL=xNew;
		}
		Error=fabs((xNew-xOld)/xNew);
		xOld=xNew;
	}while(Error>Tol);
	
	cout<<"Root found at "<<setprecision(8)<<xNew<<endl;
	cout<<"Number of iterations: "<<i<<endl;
	
	return 0;
}