\(\sqrt{2}.\left(x-1\right)+\sqrt{8}=0\)
<=> \(x\sqrt{2}-\sqrt{2}+\sqrt{8}=0\)
<=> \(x\sqrt{2}+\sqrt{2}=0\)
<=> \(\sqrt{2}\left(x+1\right)=0\)
=> x = -1
\(\sqrt{2}\left(x-1\right)+\sqrt{8}=0\)
\(\Leftrightarrow\sqrt{2}\left(x-1\right)=-2\sqrt{2}\)
\(\Leftrightarrow x-1=-2\)
\(\Leftrightarrow x=-1\)