import math


def f(x):
    return x**2 - 30

def df(x):
    return 2*x

# 牛顿方法求解方程
def NewtonSolve(fx, dfx, x0, err, N0):
    count = 0
    x1 = x0 + 1 + err
    while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
        if abs(dfx(x1)) < 1e-10:
            return None, 0
        x1 = x0 - fx(x0) / dfx(x0)
        count += 1
        if count > N0:
            return None, -1
        x0 = x1
    return x1, 1

# 查找根区间
def FindRootZone(fx,start,stop,step):
    x = start
    while x < stop:
        if fx(x) * fx(x+step) < 0:
            return x
        x += step
    return None

if __name__ == "__main__":
    err = 1e-4
    N0 = 100

    x0 = FindRootZone(f, 5, 6, 0.01)
    result,status = NewtonSolve(f, df, x0, err,N0)
    print(f"sqrt(30) = {result:.3f}")