1. ## Finding x

Hi,

What rearrangements do you make to find x?:

1/x = x - 2

Apparently the answer is x = 1 + 2^0.5

2. Originally Posted by CSG18
Hi,

What rearrangements do you make to find x?:

1/x = x - 2

Apparently the answer is x = 1 + 2^0.5

$\displaystyle \frac{1}{x} = x - 2$

$\displaystyle 1 = x^2 - 2x$

$\displaystyle 0 = x^2 - 2x - 1$

$\displaystyle 0 = x^2 - 2x + (-1)^2 - (-1)^2 - 1$

$\displaystyle 0 = (x - 1)^2 - 2$

$\displaystyle 2 = (x - 1)^2$

$\displaystyle \pm \sqrt{2} = x - 1$

$\displaystyle 1 \pm \sqrt{2} = x$.

3. Thank you very much. So you had to use completing the square. I understand now, but how would you know to use it?