Ah I'm sorry bob, but I don't think you're getting what I'm trying to say. I think I have a better way to explain it, check this out.
What I can't figure out is how the common denominator of 4a is gotten. Let me give an example. Lets say we want to add together 1/4 and 5/8. We would look of course at the multiples of 4 and find one that's equal to other denominator. So we find that 8 is the least common denominator for both fractions. We multiply 1/4 by 2/2 to get 2/8, and now we can solve.
My problem is how do we get the common denominator of 4a from -c/a? Like I said earlier, a variable without a coefficient has an implied coefficient of 1. So now we can look at -c/a as -1c/1a. How can we get the common denominator of 4 from 1, when 1 only has itself as a multiple? If both of the bases were the same we could just say it was equal to 1, divide that in half to get 5/10, get 1/2, and THEN we could have gotten the common denominator of 4. I don't see how this works.
Ah, so let me try something here.
So any variable without a coefficient has an implied value of 1 right? So based on that we can look at -c/a as -1c/1a. Now, from 1a we just get 4a/4a? That can't be right though. How can you get 4a/4a from 1a? 1 only has itself as a multiple. Do you understand what I mean?
I'm sorry but when I get stuck on something like this in math I just get fixated on it. I could just take the answer as it is but I NEED to know why it happens.
I actually watched a video that explained it that way. I'm still confused on one thing though, I want to know where the 4a that we multiply -c/a comes from. That's what I'm trying to figure out. The 4a we multiply against -c/a can't just come from nowhere right? Nothing in math can just come from "thin air" right? I mean we can't just say "We're going to multiply -c/a by 4a just because", that 4a has to come from some process and that's what I want to know.
Alright let me start from the beginning.
So we have
What I do here first is I move the "loose" number over to right.
Now we have
Now I take the coefficient onand divide it through the entire equation.
Now my method tells me that I take half of the middle term, square it and then add it to both sides.
We end up with this.
This is where I got stuck. I don't know how to get the common denominator of 4a for -c/a. I hope I wrote everything out correctly as I was doing this through memory, and keeping track of exponents and what not can be a little tough when typing it out lol.
Thanks guys. I was learning to do this through a different slightly different method however, and even though this method looks a bit shorter I'd prefer to stick with what I'm already familiar with . If you could explain how -c/a gets the common denominator of 4a in my version of the problem bob that'd be great .
I have only one question for this.
Let me write this out a little bit into the process already.
Alright so we have
What I want to know is how the common denominator for -c/a is gotten. I thought I had figured it out, but I'm pretty sure I was on the far side of mars in relation to how close I actually was to figuring it out. I THOUGHT, that since a variable with no coefficient has an implied value of 1, that I could turn -c/a into -c/2a that way, therefore gaining the ability to get the common denominator of 4a. This is wrong though I'm pretty sure.
I'm out of ideas at the moment. I need to step away from this and think some more . I would appreciate if someone could explain the process of how -c/a gets the common denominator of 4a.