A computer scientist is testing a root-finding algorithm. The scientist tests the algorithm on the equation

The computer attempts to use the iterative formula

with a starting value of $x_0=2.5$ and terminates after the third iteration, $x_3,$ has been found.

1. Find the percentage error between $x_3$ and the true value of the root.

2. Suggest an alternative iterative formula the computer could use, and evaluate this against the previous formula.

Give the percentage error found in part (a), correct to $2$ decimal places.