this imploding heart

http://underwearninja.com/tmp/sonya/math.jpg

wow... That boggles my mind. Where did that 4x come from later on? Did they breed? I like understanding math as much as I hate doing it.

Well almost as much.

there's a small mistake in the solution to that math problem by underwearninja. on the eighth line, the (x-1) should be an (x+1). then, the ninth line follows.

more: the fifth line is supposed to represent subtracting -1 from both sides and adding 3x. the "= 4x^2" part on that fifth line is kind of confusing.

finally: the 4x on the seventh line comes from taking 3x and writing it as 4x-x. now this was a clever way to put it in a form so that it would be clear how to factor, but after enough practice, one should be able to look at line six and factor it from there. there are also other information-organizing methods that make factoring a little easier, but they're too hard to explain in words.

now, the tricky part is, where did that extra solution come from? that is, why does an extraneous wrong solution pop out of our calculations even though all we've done is algebra that should always work? this is very mysterious...

(mysterious smile)
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TEHE ANSER IS CUZ THE SQYUARE ROOOOT!@!!##!, NOT MYSTERYUS 2 ME!!!@@

next stop, nerdsville!

Erfff. Yeah, my paper has the right work in step 8, just my copy to intarweb didn't follow quite right.

Line 5 is rather confusing, not sure why I wrote it that way. The 6-9 transition I did do in my head, and I work it backwards, years of tutoring forces me to write it all though (apparently it doesnt seem to force me to double check my work - I'll work on that).

As for the -1 not working despite all the correct algebra being done, Burl's anser-d that for us already =)

Whaddya mean, next stop. This IS nerdsville. I'm the mayor, homecoming queen, and treasurer of nerdsville.

Thanks for the math help, you sexy sexy nerds, you. Now, if you'd like to explain me this:

When there are negative exponents in the top and bottom of a fraction, I flip the fraction over and everything becomes positive. What if I have negative exponents in just the top or bottom? If i flip it, does that make any positive exponents that were fine as they were now become negative? None of the things on this test have anything to do with each other.

For exponents, if you "cross the line, switch the sign!"

This goes for moving from bottom to top, or top to bottom.

all of you shut up.

I hate math so much. I loathe it in fact.

But I'm not being forced to think about it and this makes me want to understand.

Thanks much with the 4x explanation. It makes me want to work some equations.
But not quite.

yeah. negative exponents. really, it all has to do with what happens when you multiply or divide by fractions since

1/x = x^(-1)

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You know, when I was doing this in class, it was my arch-nemesis. Now that it has nothing to do with me, however, I can't help but think "Game!!" It makes me want to just do a whole sheet of them... luckily for my "coolness" I do not have said sheet avaliable.