Putting an equation in quadratic form

[miahmad]

Homework Statement

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

Homework Equations

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 $$7x^2-14xz$$

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

$$7(x^2-2xz+z^2)-7z^2$$

$$7(x-z)^2-7z^2$$

Now do this for the other two terms as well.

 

[miahmad]

Thanks that helped. I can do them now.