Solve the following quadratic equations by factorization:

We have been given

$x^{2}-(\sqrt{2}+1) x+\sqrt{2}=0$

$x^{2}-\sqrt{2} x-x+\sqrt{2}=0$

$x(x-\sqrt{2})-1(x-\sqrt{2})=0$

$(x-1)(x-\sqrt{2})=0$

Therefore,

$x-1=0$

$x=1$

or,

$x-\sqrt{2}=0$

$x=\sqrt{2}$

Hence, $x=1$ or $x=\sqrt{2}$.