\(x^2+4x+2=0\)
\(\Leftrightarrow\left(x^2+4x+4\right)-2=0\)
\(\Leftrightarrow\left(x+2\right)^2=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=\sqrt{2}\\x+2=-\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}-2\\x=-\sqrt{2}-2\end{matrix}\right.\)
\(\Leftrightarrow x^2+4x+4-2=0\)
\(\Leftrightarrow\left(x+2\right)^2=2\)
\(\Leftrightarrow\left[{}\begin{matrix}x+2=\sqrt{2}\\x+2=-\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\sqrt{2}-2\\x=-\sqrt{2}-2\end{matrix}\right.\) ( TM )
Vậy tập nghiệm của pt đã cho là \(S=\left\{\sqrt{2}-2;-\sqrt{2}-2\right\}\)
