Putting an equation in quadratic form

miahmad

1. The problem statement, all variables and given/known data

Could someone please explain how to go about putting an equation in to quadratic form.
e.g:
Q(x,y,z)=7x^2-2y^2-40z^2-14xz+20yz.

2. Relevant equations



3. The attempt at a solution

I know it equals 7(x-z)^2 -2(y-5z)^2 +3z^2. dnt know how to get there though

Mentallic

Firstly look at [tex]7x^2-14xz[/tex]

This becomes [tex]7(x^2-2xz)[/tex] and now you just need to complete the square on that factor. Remember to subtract whatever you added to complete the square.

[tex]7(x^2-2xz+z^2)-7z^2[/tex]

[tex]7(x-z)^2-7z^2[/tex]

Now do this for the other two terms as well.

miahmad

Thanks that helped. I can do them now.