# Quadratic surfaces question

1. Oct 14, 2011

### JamesGoh

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

Write the following quardatic surface equation as a sum of multiples of
squares of independent linear functions

$x^{2}+4y^{2}+56z^{2}+2xy+4xz+28yz$

2. Relevant equations

3. The attempt at a solution

nb. there is no answer provided by the tute, but from all the previous exercises, it should
be in the form of something like $(ax + by -cz)^{2} + (dx + ey -fz)^{2} + g^{2}$

My problem is that I have no effective and quick way to solve these sorts of problems using the complete the squares method.

I would have to spend hours trying to find a combination that will make the equation balance out

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