$(15$ points$)$

For the following nonlinear equation:

$x^3-8x+\sqrt[\phantom{2}]{x}=110$

Use a starting guess of $x=12$ and solve the equation using fixed point iteration.

For each iteration $(n)$ starting with the initial guess $)=(0$ calculate and print the following information in a table:

$n_{,}{x}_{,}f(x{)}_{,}g(x{)}_{,}d\frac{g}{d}{x}_{?}$