How can I complete the square for a three variable expression

Question

For $x^2+y^2+z^2-4yz$ is it possible to complete the square?

I've managed to get $x^2+(y-z)^2+3yz$

Answer 1

Yes $$x^2+(y-\frac{z}{2})^2+\frac{3}{4}z^2$$

Answer 2

The eigenvalues of $\begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & -2 \\ 0 & -2 & 1 \end{pmatrix}$ are $3$, $1$, $-1$, there should be one negative term.

$$x^2+y^2+z^2-4yz=x^2+\frac{3}{2}(y-z)^2-\frac{1}{2}(y+z)^2$$