Getting it to be in "y = " form

[Cohiba]

y^2 - 2y = 1+x^2

How can you that into y = **** form

I started like:

y^2 - 2y = 1+x^2
y^2 = 2y + x^2 + 1
y = sqrt(2y + x^2 + 1)

but then i saw that I had a y inside the sqrt. Any way to do this?

[Alvaro]

Do you know how to solve second degree polynomial equations? You can do this either by "completing squares" (I am not sure if that's its English name) or you can write it as Ay^2 + By + C = 0 and then remember a simple formula that gives you the roots.

Either way would work. Just do the manipulations using x as if it were constant.

I'll write the solution using the first method ("completing squares") for you:
y^2 - 2y looks like part of the expansion of (y-1)^2 = y^2 - 2y + 1, doesn't it? Let's just add 1 on both sides of the equation so we complete our square (y-1)^2.

y^2 - 2y + 1 = 1 + x^2 + 1
(y-1)^2 = 2 + x^2
y-1 = sqrt(2 + x^2)
y = 1 + sqrt(2 + x^2)

[crackity]

not trying to be a stickler but:

y^2 - 2y + 1 = 1 + x^2 + 1
(y-1)^2 = 2 + x^2
y-1 = +/- sqrt(2 + x^2)
y = 1 +/- sqrt(2 + x^2)

[Alvaro]

Sure, I always take sqrt to mean both signs, but I know this is not very standard. Sorry about that.

[MXP]

Alvaro, you're English is almost as good as your math. You're right that the term is "Completing the Square" in English

[Alvaro]

Alvaro, you're English is almost as good as your math.

Well, is looks like your English isn't.

I don't really know how to pronounce English, which makes it much easier for me to distinguish between "your" and "you're", between "there", "they're" and "there", etc. And American girls love the weird accent.

[MJOLNIRdragoon]

alvaro, where are you from?

ok,
y^2 - 2y = 1+x^2
y - 2y = sqrt(1 + x^2)
y - 2y = sqrt(1) + x
-y = sqrt(1) + x
y = -sqrt(1) - x?

Or would taking the squaring off of the first y, would that square, square root, or do nothing to the 2y? if im wrong (which now that i think of it, seems likely) about it not doing anything to the 2y, then my mention is way off.

assuming by sqrt() you mean the square root, and the way we did that is correct, y should = the negative square root of 1 minus x. someone mind double checking me?

[Alvaro]

alvaro, where are you from?

Logroño, Spain.

Yes, "sqrt" means "square root". The rest of your post is too wrong to answer.

[MJOLNIRdragoon]

lol, yeah thats what I figured (about my post)

[MXP]

Alvaro, you're English is almost as good as your math.

Well, is looks like your English isn't.

I don't really know how to pronounce English, which makes it much easier for me to distinguish between "your" and "you're", between "there", "they're" and "there", etc. And American girls love the weird accent.

What an ironic typo

And you foreigners take all the best girls. Nobody finds the California dialect attractive because everyone on TV already speaks like we do

[t i l e x]

I'm sure my French accent and my awesomeness would seduce them all