def METHOD_NAME(self, xp, tail):
    """ Quadratic series expansion solution to return seed LDF for tail"""
    arr = self.decay ** xp.arange(1000)
    a = xp.sum(arr ** 2)
    b = xp.sum(arr)
    c = -xp.log(tail)
    return (-b + xp.sqrt(b ** 2 - 4 * a * c)) / (2 * a)