How to find $x_1$?

Question

let $f(x) =x^2-5$ for $x \in \mathbb{R}$ . Let $x_0 =1$ . If $\{x_n\}$ denotes the sequence of iterates defined by the newton -raphson method to approximate a solution of $f(x)=0$ . Find $x_1$

My attempt : i know the The Newton-Raphson Method is:

$$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$

Now by applying this formula on the given question

$$x_{n+1} = x_n - \frac{x_n^2-5}{2x}$$

After that im not able to proceed further

Answer 1

Your iteration should be $$ x_{n+1} = x_n - \frac{x_n^2-5}{2x_n} = \frac{x_n^2+5}{2x_n} = \frac{x_n}{2} + \frac{5}{2x_n} $$ So for $n=0$ can you finish the problem?

Answer 2

$$x_1 = x_0 - \frac{f(x_0)}{f'(x_0)} = 1-\frac{f(1)}{f'(1)} = 1-\frac{-4}{2} = 3.$$