[tex]-4x^2-8x-2=0\\\\-4\big(x^2+2x+\frac{1}{2}\big)=0\quad|:(-4)\\\\x^2+2x+\frac{1}{2}=0\\\\x^2+2x+1-\frac{1}{2}=0\\\\
\big(x^2+2x+1\big)-\frac{1}{2}=0\\\\
\big(x+1\big)^2-\frac{1}{2}=0\\\\\big(x+1\big)^2=\frac{1}{2}\quad|\sqrt{(\ldots)}\\\\\\x+1=\sqrt{\frac{1}{2}}\qquad\vee\qquad x+1=-\sqrt{\frac{1}{2}}\\\\\\
\boxed{x=\sqrt{\frac{1}{2}}-1\qquad\vee\qquad x=-\sqrt{\frac{1}{2}}-1}[/tex]
or in different forms:
[tex]\boxed{x=\dfrac{1}{\sqrt{2}}-1\qquad\vee\qquad x=-\dfrac{1}{\sqrt{2}}-1}\\\\\\
\boxed{x=\dfrac{\sqrt{2}}{2}-1\qquad\vee\qquad x=-\dfrac{\sqrt{2}}{2}-1}[/tex]
