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Hello internet! Oscar Veliz here showing you how to use another approach to finding roots called fixed point iteration. So how does fixed point iteration work? First if were given an f of x, set it to zero, and then write it so that we have x is equal to something. Then well labeled the left side as x sub n plus one and the right side with x sub n. Then well go ahead and pick and x one and plug it into our equation and repeat it with every new x until it converges. So if were given an example of where we want to find where x squared minus x minus one is equal to zero, heres how well do it. So using fixed point iteration well set x in terms of something. And theres a few ways to do that. One way is to say that x squared is equal to x plus one and therefore x is equal to one plus one over x. So x sub n plus one is equal to one plus one over x sub n We can also say this; that x squared minus x is equal to one. Therefore factor out an x and divide by that we can say x is qual to o
