$2x^2+2+\frac{2\sqrt{(x-1)^2(x^4+x^2+1)} }{|x-1|}=16$
$2x^2+2+\frac{2|x-1|\sqrt{(x^4+x^2+1)} }{|x-1|}=16$
$2x^2+2+2\sqrt{(x^4+x^2+1)}=16$ $(x\not= 1)$
$x^2+\sqrt{(x^4+x^2+1)}=7$
$\sqrt{(x^4+x^2+1)}=7-x^2$
$x^4+x^2+1=x^4-14x^2+49$
$15x^2=48$
$x=\pm \sqrt{\frac{48}{15} } $
$x=\pm 1.79$