import numpy as np


def equation(x):
    return 2 * x**3 + 2 * x**2 - 2 * x - 7


def derivative(x):
    return 6 * x**2 + 4 * x - 2


def newton_method(initial_guess, tolerance=1e-3, max_iterations=100):
    x = initial_guess
    for iteration in range(max_iterations):
        delta = equation(x) / derivative(x)
        x_k = x - delta
        #x -= delta

        if equation(x_k) * equation(x_k + np.sign(x_k - x)*tolerance) < 0:
            return x_k, iteration

        x = x_k
    raise ValueError("The method did not converge")

# Solve the equation using Newton's method
initial_guess = 1.0
root, iteration = newton_method(initial_guess)
print("Root:", root)
print("Value at the root:", equation(root))
print("Iterations:", iteration)