EXTREME quintic equation! (very tiring)

We will solve an extreme quintic equation x^5-5x+3=0 by brute force factoring. This is a solvable quintic because we can factor the quintic expression = quadratic * cubic by using the undetermined coefficients method. Then we can use the quadratic formula to solve the quadratic equation (and we will get a negative golden ratio). For the cubic, I will not use the cubic formula but I will show you the Lagrange Resolvent approach and we can find its real solution. Let me know if you can find the complex solutions to the cubic equation. 🛍 Get a 1.618 t-shirt: https://bit.ly/1618shirt 10% off with the code "WELCOME10" Try another famous extreme algebra problem 👉    • Extreme Algebra Question  (#patience)   Solve this quintic equation by Newton's method 👉    • Newton's method (introduction & example)   Another equation by the Lagrange Resolvent 👉    • solving a cubic equation by completing the...   ---------------------------------------- **Thanks to ALL my lovely patrons for supporting my channel and believing in what I do** AP-IP Ben Delo Marcelo Silva Ehud Ezra 3blue1brown Joseph DeStefano Mark Mann Philippe Zivan Sussholz AlkanKondo89 Adam Quentin Colley Gary Tugan Stephen Stofka Alex Dodge Gary Huntress Alison Hansel Delton Ding Klemens Christopher Ursich buda Vincent Poirier Toma Kolev Tibees Bob Maxell A.B.C Cristian Navarro Jan Bormans Galios Theorist Robert Sundling Stuart Wurtman Nick S William O'Corrigan Ron Jensen Patapom Daniel Kahn Lea Denise James Steven Ridgway Jason Bucata Mirko Schultz xeioex Jean-Manuel Izaret Jason Clement robert huff Julian Moik Hiu Fung Lam Ronald Bryant Jan Řehák Robert Toltowicz Angel Marchev, Jr. Antonio Luiz Brandao SquadriWilliam Laderer Natasha Caron Yevonnael Andrew Angel Marchev Sam Padilla ScienceBro Ryan Bingham Papa Fassi Hoang Nguyen Arun Iyengar Michael Miller Sandun Panthangi Skorj Olafsen Riley Faison Rolf Waefler Andrew Jack Ingham P Dwag Jason Kevin Davis Franco Tejero Klasseh Khornate Richard Payne Witek Mozga Brandon Smith Jan Lukas Kiermeyer Ralph Sato Kischel Nair Carsten Milkau Keith Kevelson Christoph Hipp Witness Forest Roberts Abd-alijaleel Laraki Anthony Bruent-Bessette Samuel Gronwold Tyler Bennett christopher careta Troy R Katy Lap C Niltiac, Stealer of Souls Jon Daivd R meh Tom Noa Overloop Jude Khine R3factor Jasmine Twinkletoes ---------------------------------------- 💪 If you would also like to support this channel and have your name in the video description, then you could become my patron here   / blackpenredpen