Using the Newton$-$Raphson iteration find the root of the equation x$+$x$2=7.$ With an initial guess of x$=7$ compute the number of iterations required for the error in the root to be below $1\mathrm{.}0$e$6.$

This is my code, the root is correct but the number of iterations is off by one $($it should be $5$ but I keep getting $6)$:

import math

def f$($x$)$:

return math.sqrt$($x$)+$ x$**2-7$

def df$($x$)$:

return $1/(2*$ math.sqrt$($x$))+2*$ x

def newton$\_$raphson$($x$0,$ tol, full$\_$ouptut$=$True$)$:

num$\_$iter $=0$

error $=$ tol $+1$

while error $>$ tol:

x$1=$ x$0-($f$($x$0)/$ df$($x$0))$

error $=$ abs$($x$1-$ x$0)$

x$0=$ x$1$

num$\_$iter $+=1$

return x$0,$ num$\_$iter

x$1=7$

tol $=1$e$-6$

root$3,$ num$\_$iter $=$ newton$\_$raphson$($x$1,$ tol, num$\_$iter$)$

print$("$Newton$-$Raphson method root and num$\_$iter:", root$3,$ num$\_$iter$)$