Michael P. answered • 10/29/14

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Mary Anne,

You are correct that the initial equation is x = 1/x + 1

You then rearrange the equation into a quadratic by

1. Multiply both sides of the equation by x to get x^2 = 1 + x

2. Subtract x and 1 from both sides to get x^2 - x - 1 = 0

3. Using the quadratic formula (where a=1, b=-1, c=-1), you find that possible values for x are (1 + sqrt(5)) / 2 and (1 - sqrt(5)) / 2

4. Since the answer must be positive and real, then x = (1 + sqrt(5)) / 2 (or 1.618) is your solution.