Solve the following equation by factorization:

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

Given,

$\Rightarrow x^2 - (1 + \sqrt{2})x + \sqrt{2} = 0 \\[1em] \Rightarrow x^2 - 1x - \sqrt{2}x + \sqrt{2} = 0 \\[1em] \Rightarrow x(x - 1) - \sqrt{2}(x - 1) = 0 \\[1em] \Rightarrow (x - \sqrt{2})(x - 1) = 0 \\[1em] \Rightarrow (x - \sqrt{2}) = 0 \text{ or } (x - 1) = 0 \text{ [Using Zero-product rule] } \\[1em] \Rightarrow x = \sqrt{2} \text{ or } x = 1.$

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