Help with understanding what his algorithm does and how it comes up with the numbers

[soldatik21]

Just starting to lean about algorithm and programming and professor gave us this question and told us to figure out what i does thanks for the help

#include <cstdlib>
#include <iostream>
#include <cmath>
using namespace std;
int main( )
{
  double a, x_old, x_new;
  cout << "Enter a positive DECIMAL number => ";
  cin >> a;
  x_old = 1;
  x_new = 0.5*( 1 + a );
  while( fabs(x_old - x_new) >= 0.00005)
  {
    x_old = x_new;
    x_new = 0.5*( x_old * x_old + a )/x_old;
  }
  cout << "\nThe value that you are seeking is " << x_new << endl;
  cout << "Press the enter key to continue ...";
  cin.get();
  return 0;
}