kill(all)$

van=facebook.com/LearningCalculus$

f(x):=x^4-22*x^3 + 171*x^2 - 551*x +625 - sqrt(x+sqrt(x));

newton(t):=bfloat(subst(t,x,x-f(x)/diff(f(x),x)));

X:newton(2.7690936625710440471271392319699700916831663407495b0);

ceiling(X);

factor(f(x));