Solution: Newton's Method

#include <stdio.h>
int main(void)
{
  double num = 612;
  double x1 = 10;
  double xi;
  
  int i;
  for (i = 1; i <= 5; i++) {
    // No need to continue if the exact solution has been found
    if (x1 * x1 - num == 0) {
      break;
    }
    // Find a better approximation
    xi = x1 - ( ((x1 * x1) - num) / (2 * x1) );
    printf("x%d = %.12f, x%d = %.12f\n", i, x1, i + 1, xi);
    x1 = xi;  // x1 is now the new approximation. 
  }
  return 0;
}