Question

y^2+3yz+8z-4x=0 solve for z?

Answer 1

If the last one 'made sense' why are you confused about how to do this one?

Answer 2

beacuse i'm a slow learner and this one is different. sorry if i'm bad at math. that's kinda why i'm asking for help

Answer 3

This one isn't any different.

Answer 4

islote all the terms that have a z factor in them.

Answer 5

Isolate rather

Answer 6

yes it is! there's exponents

Answer 7

None of the exponents are on the z..

Answer 8

so it'd be y^2-4z=3yz-8z?

Answer 9

Ok, do you know what I mean by isolate the terms with z factors?

Answer 10

no

Answer 11

Ok. Do you know what I mean by 'term'?

Answer 12

Yes, I'm not *that* oblivious

Answer 13

Ok so which terms don't have z factors?

Answer 14

I don't get what you mean by isolate them, I thought that's what I did

Answer 15

I'm not meaning to be insulting. I just need to know what you know and what I should explain

Answer 16

No no I understand, I'm just frustrated is all
So the z terms are 3yz and the 8z

Answer 17

Yes. Good.

Answer 18

Now to isolate them means to subtract (or add) all the other terms that don't have a z to the other side of the equal sign.

Answer 19

Oh, you actually did that before but I got confused because you said -4z instead of -4x

Answer 20

I'm sorry. You were right so far:

\[y^2 - 4x = -3yz - 8z\]

Answer 21

Oh whoops sorry, mistype. That makes more sense then cuz I was confused cuz I thought I did it right lol

Answer 22

Now. The next step is to factor out the z from each of the terms that have it.

Answer 23

So instead of -3yz - 8z we have z(-3y - 8)

Answer 24

Okay got that

Answer 25

we divide the z away from each term and instead put it out in front

Answer 26

because you can see that
\[z(-3y - 8 ) = -3yz - 8z\]

So we are just going in reverse

Answer 27

k

Answer 28

Now to get the z by itself we just divide both sides of the equal sign by the non-z factor

Answer 29

So it'd be z(3y-8)/-4-y^2? Or am I totally lost?

Answer 30

Right track. Wrong factor

Answer 31

Instead divide both sides by (-3y-8)

Answer 32

the factor next to the z we want to get rid of, so we divide it off, but we have to divide both sides to keep it equal

Answer 33

Oh because their the terms you factored the z from? Got it

Answer 34

\(y^2 - 4x = z(-3y - 8)\)\[\implies \frac{y^2 - 4x}{-3y - 8}= z\frac{-3y-8}{-3y-8}\]

Answer 35

and the fraction on the left has the same value on top and bottom, so that is just 1 now.

Answer 36

err fraction on the right, sorry

Answer 37

\[\implies \frac{y^2 - 4x}{-3y - 8}= z \]

Answer 38

Get it?

Answer 39

Yes I think so

Answer 40

Could you help me with more of my packet?? You're explaining better than any of my teachers ever have. If you don't have time, that's totally fine tho

Answer 41

Ok so here's a summary of what we did. You should write this down in your notes. Then see if you can do it for yourself the next time.

Solving equation for 'z' (could be any letter)

1) Isolate the terms that have a factor of z by adding/subtracting the z terms to one side and the non-z terms to the other side.

2) factor out the z from each term, putting it in front of parens and dividing the z off each term

3) divide both sides by the factors being multiplied by your z

Answer 42

I'm happy to help

Answer 43

feel free to ask more questions

Answer 44

Wonderful! Thank you. I'm new to this site, so do you want the q's separately or just on here?

Answer 45

separately is better otherwise it gets lagged when the thread gets too long