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This is a graph of the original equation, in the form x = g (x), I am investigating: 0 = 3x^5 - 3x + 1 Graph of Re-arranged equation: x = 3x^5 + 1 3 The Rearrangement method, firstly, draws a vertical line between the 2 curves. When it reaches the second curve, another line is drawn horizontally. This carries on until a value of the function is calculated to the required accuracy. However, for this method to work, the gradient of the curve, at the starting point, must be between -1 and 1. I am going to investigate the root in the middle. Below is a zoomed-in view of the middle root of the rearranged equation. Here it is clear that there is a repeated answer of 0.33773. Therefore the root is 0.337735 ±0.000005. This could also be done without the use of a...

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