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This is an alternate method for solving equations, which, if it can be started, always produces a solution between the initial starting points.
Method:
To solve equation f(x)=0.
To start you must find two points, a and b, such that f is positive at one and negative at the other.
Suppose f(a)>0 and f(b)<0.
Step:
Examine .
If it positive replace b by 
.
Repeat this step until the resulting a and b are indistinguisable to the accuracy you desire.
The resulting a or b is your solution.
Notice that the distance between a and b after n steps is |b - a|2-n.