# Homework Help: Putting an equation in quadratic form

1. Apr 28, 2010

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

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

2. Apr 28, 2010

### 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.

3. Apr 28, 2010