I need to complete the square on the following equation, can anyone help?
+ + - x'+ z'=0
I will do the first third (the x part)
1: gather all of the x,y and z stuff together this gives
First we factor a 3 (the lead coefficient of the x squared term) out of only the x terms this gives
Now we take half of the coefficient of the x term and square it.
Now we add this inside the parentheses on the left to get
but we also have to add this to the other side so we don't change the equation. Also don't forget to multiply it by the 3 out side the parenthesis to get
Now factor the x's to get
Now you just need to do the z's the y is already a perfect square.
As long as you are using the correct expression for z'' then yes. Your post 7 definition of z'' does not have the correct expression. (Note that your discussion with TheEmptySet has changed what z'' should be.)
-Dan
Edit: Okay, you edited post 7. I didn't see that. (Please don't do that or mention that you have done so, else it causes confusion, like in this instance.)
Yes, your substitutions are correct.