Completing the square of: $y^2-xz$

Question

How can I complete the square of the following monomial: $y^2-xz$ to obtain the sum of 3 squares of the form: $y'^2-z'^2-x'^2$. Any suggestions for finding $x',y'$ and $z'$??

Answer 1

You just can't do that. The closest thing you can get is $y'^2+x'^2-z'^2$. For that, take $x'=\frac{x-z}2$, $y'=y$, and $z'=\frac{x+z}2$.