Question

= x + 8 " alt=" \sqrt{2x} + 12 = x + 8 " align="absmiddle" class="latex-formula">

Answer 1

First note that $x\ge0$; otherwise $\sqrt{2x}$ is undefined as long as we're only looking for real solutions.

We can write

$\sqrt{2x}+12=x+8$
$\sqrt{2x}=x-4$
$2x=(x-4)^2$
$2x=x^2-8x+16$
$x^2-10x+16=0$
$(x-8)(x-2)=0$

$\implies x=8,x=2$