/sci/ - Science & Math

>[math] x^2 - 2x + 2 > 0 [/math]
My solution
>[math] (x-1)^2 > -1} [/math]
Because the exponent is odd, the left hand side of the equation will always be positive, and so any value in the set of reals will work for x.

But the solution here, https://etoix.wordpress.com/category/calculus-by-spivak/page/2/ , has a different answer. How did they arrive at that? Pic related. Ultimately we both had the same final answers, all reals, but I'm curious as to how I may have arrived at the same answer differently. My method for arriving at this answer was a straightforward completion of the square. It looks as though this person used a similar method, but I don't understand how they could've done anything differently.