Approximation

Approximate value of the root of x^3-3.25x^2+x-0.063 near 3 to 110 digits

x =     3.00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
 f(x) = 0.68700000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
x =     2.91917647058823529411764705882352941176470588235294117647058823529411764705882352941176470588235294117647058824
 f(x) = 0.03703357162141257887237940158762466924486057398738041929574598005292082230816201913291268064319153266843069408
x =     2.91429729361430126416635046525103867489956516746755286314020454753268560803719447857518875108761294400091181521
 f(x) = 0.00013099811615088857638069577827038142015720403700761287544078364489037248881217184377355822979045595886402196
x =     2.91427991168366103139673367720949542259929189468785141694361079092291900451120742003934794158293356377232109192
 f(x) = 0.00000000165957048187727867202779247030465410272503029069047031605285358681065853713382830040510430756760482225
x =     2.91427991146344969731430820521214129356230810888010502592571871357388325429468243968102085544191924156988128949
 f(x) = 0.00000000000000000026636445115545516368981428092914856743014373003195355109725987014543933271527729230981974784
x =     2.91427991146344969727896383641283993719396615637022493137732149757025063099235773911075494842210925033558754363
 f(x) = 0.00000000000000000000000000000000000000686178945346391272928433810509021073997943484114613291420620729311574550
x =     2.91427991146344969727896383641283993719305565342580295729325455579843735535238013087959511346836032331096598663
 f(x) = 0.00000000000000000000000000000000000000000000000000000000000000000000000000000455364989293092134075384876996290
x =     2.91427991146344969727896383641283993719305565342580295729325455579843735535237952664775974472142709480474322882
 f(x) = -0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000