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Fixed Point Equations

The chapter in question is about Iteration.(x2 means x squared).
It talks about the Fixed point rule. It describes a fixed opint equation as
x2 + 1/8 = x; that is x2 - x + 1/8 = 0

It then gives another example:
Determine the fixed points of the function f(x) = -1/8x2 + 11/8x + 1/2
and states that the fixed point equation is:

-1/8x2 + 11/8x + 1/2 = x; that is, x2 - 3x - 4 =0
I don't know how this has been achieved - I did try adding the x fractions and multiplying by 2 and then 1/2(-8) =4.

Another example says:
The fixed point equation is

1/8x2 - x + 7 = x; that is, x2 - 16x +56 = 0

Then finally:
f(x) = -1/4x2 + 4/3x + 5/3

The question says-use algebra to find the fixed points of f, which I assume to mean
using a quadratic equation as above.
I've tried adding the similar fractions and have come up with a possible answer

x2 +12x + 20 = 0

Solution Summary

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