I have trouble solving this first degree equation:
$ 2(x-1) = \sqrt{2} (x + 1) - 1$
I can't see a way to factorize this, so using a distributive aproach I get this:
$ 2x = x \sqrt{2} + \sqrt{2} + 1$
Now my issue is that, how do I get rid of $ \sqrt{2} $ terms ? I tried to squared the whole equation this way: $ 2x² = (x \sqrt{2})² + 3$
But now I'm stuck, the expected result is (a non-detailed results is given, hence I'm looking for how to continue solving):
$ x = \frac{4 + 3 \sqrt{2}}{2} $
Am I not using the correct way to solve this, or I'm mistaking in the evaluation of: $(x \sqrt{2})²$ ?
Or should I even start by squaring both sides to this way:
$ 2(x-1)² = (x + 1) - 1$
Thanks.