Hello! I'm having trouble understanding the method/reasoning behind finding the root of an equation though iterative convergence. x2 - 4x + 1 = 0 x2 = + 4x - 1 x = 4 - 1/x I can understand that once we input a 'root' the equation will equal be equal on both sides. (Due to the remainder theorem) However I can't grasp why it converges to a root in all cases... I also can't seem to understand how if we set x as 3, then we get x or x0 as 3.667... x = 4 - 1/(3) = 3.667 I obviously understand the equation it just doesn't quite fit how x is equal to 2 different values neither of which are a root? How would it account for a equation that would have a 'higher' Y value for: x0 . Which 'goes past' the root? (I've drawn a blue line over the graph).