Is it possible to solve this?

I feel kinda dumb for not knowing what to do here, but I know my math knowledge is somewhat lacking, and I figure people here know what they are doing, so..

This isn't homework or anything, I just wrote random numbers down on a dry erase board and tried to find an answer. I'm looking for the value of y.

(7x-3y)^2-6 = 7

So far I've done..

49x^2-42xy+9y^2 = 13
49x^2-y(42x)+y(9y)-13 = 0
49x^2-13 = y(42x)-y(9y)

But I'm not sure where to go from here, or if it's even possible to.

Thanks for the help.

There's a math help thread you know!

Code:

(7x-3y)^2-6 = 7
(7x-3y)^2 = 13
7x - 3y = sqrt(13)
-3y = sqrt(13) / (7x)
y = -[sqrt(13) / (21x)]

Oh wow, thanks.

I was just over thinking it.

Didn't realize there was a math help thread, sorry. It's right on the front page too, blah.

Thanks again though.

There's a math help thread you know!

Code:

(7x-3y)^2-6 = 7
(7x-3y)^2 = 13
7x - 3y = sqrt(13)
-3y = sqrt(13) / (7x)
y = -[sqrt(13) / (21x)]

Shouldn't it be
y = ([sqrt(13)] - 7x)/-3
?

It should go:

Code:

(7x-3y)^2-6 = 7
(7x - 3y)^2 = 13
7x - 3y = sqrt(13)
-3y = sqrt(13) - 7x
y = ([sqrt(13)] - 7x)/-3

Since:

7x - 3y = -3y + 7x

Hm.

Wouldn't it be..

Code:

(7x-3y)^2-6 = 7
7x-3y = sqrt(13)
-3y = sqrt(13)-7x
y = -((sqrt(13)-7x)/3)

Or am I doing something wrong?

Hm.

Wouldn't it be..

Code:

(7x-3y)^2-6 = 7
7x-3y = sqrt(13)
-3y = sqrt(13)-7x
y = -((sqrt(13)-7x)/3)

Or am I doing something wrong?

I think this is right.

Hm.

Wouldn't it be..

Code:

(7x-3y)^2-6 = 7
7x-3y = sqrt(13)
-3y = sqrt(13)-7x
y = -((sqrt(13)-7x)/3)

Or am I doing something wrong?

Yeah. I just distributed the -3.

(I didn't say that 7 divided by 3 was 21....YOU DIDN'T SEE ANYTHING! -Fixes it-)

Yeah. I just distributed the -3.

(I didn't say that 7 divided by 3 was 21....YOU DIDN'T SEE ANYTHING! -Fixes it-)

CRAP. I JUST REALIZED I MULTIPLIED THE SQRT(13) BY -3 TOO.


-Fixes again-

you are forgetting that sqrt[(7x-3y)²] = |7x-3y|, so you would have:

y = (7x-sqrt(13))/3
or
y = (7x+sqrt(13))/3

you are forgetting that sqrt[(7x-3y)²] = |7x-3y|, so you would have:

y = (7x-sqrt(13))/3
or
y = (7x+sqrt(13))/3

Oh crap, can't solve it that way.



ugly. Does not exist at


(Which is a really low number, btw)

Uh, I think you put the wrong number in the denominator. You put what would be C instead of A.

Wouldn't it actually be... (Sorry it's so messy, I don't really understand how to use mathurl)..

Code:

(-42x +/- sqrt((42x)^2-4*9*(13-49x^2))) / (2 * 9)
(-42x +/- sqrt(1764x^2-36(13-49x^2))) / 18
(-42x +/- sqrt(1764x^2-468+1764x^2)) / 18
(-42x +/- sqrt(2(1764x^2)-468)) / 18
(-42x +/- sqrt(3528x^2-468)) / 18

Not sure if I can go further.

Um. You foiled it wrong. It's supposed to be 49x^2 - 42xy + 9y^2.

So:
y = (-42x +/- sqrt((42x)^2 - 4*-9*(13 - 49x^2))) / (2 * -9)
= (-42x +/- sqrt(1764x^2 + 468 - 1764x^2)) / -18
= (-42x +/- sqrt(468)) / -18
= (-42x +/- 6 sqrt(13)) / -18
= (7x +/- sqrt(13)) / 3

... which is the same answer you get from completing the square, if you account for the +/-:

(7x - 3y)^2 = 13
7x - 3y = +/-sqrt(13)
-3y = -7x +/- sqrt(13)
y = (7x +/- sqrt(13)) / 3

Shouldn't it be
y = ([sqrt(13)] - 7x)/-3
?

It should go:

Code:

(7x-3y)^2-6 = 7
(7x - 3y)^2 = 13
7x - 3y = sqrt(13)
-3y = sqrt(13) - 7x
y = ([sqrt(13)] - 7x)/-3

Since:

7x - 3y = -3y + 7x

Oh gawd now I'm scared of myself o.o

I'm also ashamed of Taiketo for not catching that mistake. Your syntax in the last line is wrong though.

Oh, sweet.

I was thinking you'd get the same answer, but I wasn't sure why I wasn't.

EDIT : Yeah, I feel dumb for not noticing it. Well, I mean... I noticed your mistake, but by the time I posted someone else had also. I didn't notice the other mistake, in that I took the a, b, c, etc for the quadratic formula from the post above me without checking them, which is why I was using 9 instead of -9.

Thanks for the continued help everyone, heh.

Oh gawd now I'm scared of myself o.o

I'm also ashamed of Taiketo for not catching that mistake. Your syntax in the last line is wrong though.

Bleh. I hate syntax crap.

Oh, sweet.

I was thinking you'd get the same answer, but I wasn't sure why I wasn't.

EDIT : Yeah, I feel dumb for not noticing it. Well, I mean... I noticed your mistake, but by the time I posted someone else had also. I didn't notice the other mistake, in that I took the a, b, c, etc for the quadratic formula from the post above me without checking them, which is why I was using 9 instead of -9.

Thanks for the continued help everyone, heh.

Such a Renaissance man, Sha. <3

Interesting that I did not catch that one. Harr.

Does not exist at

It perfectly well exists at that condition.

It perfectly well exists at that condition.

If you notice, my whole calculation's horribly wrong. It's supposed to be +9y² and the denominator isn't supposed to be the constant c, but the constant a.