(adsbygoogle = window.adsbygoogle || []).push({}); 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

[itex]x^{2}+4y^{2}+56z^{2}+2xy+4xz+28yz[/itex]

2. Relevant equations

3. The attempt at a solution

Please see attachment.

nb. there is no answer provided by the tute, but from all the previous exercises, it should

be in the form of something like [itex](ax + by -cz)^{2} + (dx + ey -fz)^{2} + g^{2}[/itex]

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Quadratic surfaces question

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**