$$\sqrt{ 2 } x+1+1=x$$
$x=-2\sqrt{2}-2\approx -4.828427125$
$$\sqrt{2}x+2=x$$
$$\sqrt{2}x+2-x=0$$
$$\sqrt{2}x-x=-2$$
$$\left(\sqrt{2}-1\right)x=-2$$
$$\frac{\left(\sqrt{2}-1\right)x}{\sqrt{2}-1}=-\frac{2}{\sqrt{2}-1}$$
$$x=-\frac{2}{\sqrt{2}-1}$$
$$x=-2\sqrt{2}-2$$
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