Quadratic equation without numbers?

[lax1113]

Quadratic equation without numbers??

How would one go about solving an equation such as B²X²+2ABCX-ABC² for the value of x that equals zero?

All of the letters are constants except for X, so would this be a quadratic equation problem.?

The solution in the book is somehow


x=(AC/B){\sqrt{1+(B/A)})-1}


that -1 on the end is not the the negative 1 power, but -1

 

[Dick]

Yes. It's just a quadratic equation. Take the quadratic formula and put 'a'=B^2, 'b'=2ABC and 'c'=-ABC^2. Then simplify.

 

[lax1113]

ok thanks dick,
I did that before but simplifying it I could never get down to an answer that looked the same. Seemed like it would be some hardcore manipulation to get it to be that.

 

[daschaich]

With the answer in front of me, I was able to do it in one step. Feel free to post your work if you continue having difficulty.

 

[lax1113]

dasch...

Are you a savant? just kidding bud, but seriously you can simplify that just like that? I honestly have used 3 maybe 4 pieces of computer paper, and its just not working out for me. Do you have an aim or something that I could communicate with you with that i could get a step through of this? Or maybe just using pm's here or whatever.

 

[Dick]

dasch...

Are you a savant? just kidding bud, but seriously you can simplify that just like that? I honestly have used 3 maybe 4 pieces of computer paper, and its just not working out for me. Do you have an aim or something that I could communicate with you with that i could get a step through of this? Or maybe just using pm's here or whatever.

You would make it a lot easier for people to help you if you would post what you got and how you are trying to simplify it. It's not THAT hard.

 

[lax1113]

sorry,
That approach does seem a lot better, just hard to write out the long strings of numbers sometimes on this site. And as to the being hard thing, I am only a high schol student, most of you are college grads and teachers/professors, so it might seem simple to many of you, but imagine the first time you ever did it, most likely different. Anyway,


After quadratic equation i got this.

(-AC +/- \sqrt{(AC)^2-(B)(-AC^2}) all divided by B


I took the 4 inside the square root and the 2^2 outside of the root as a 2, then the 2 in from tof -AC and the 2 on the denominator all canceled out.

Now where to?

 

[Dick]

You are already almost done. The square root is sqrt((AC)^2+(AC)^2*B/A), right? I just pulled (AC)^2 out of both terms. Now factor AC out of the square root.

 

[lax1113]

woooooow...

I really cannot believe I looked at this for this long and never saw that. Thank you very much, I don't know why i wasn't getting that, but now i see it, and finally got it!

 

[Dick]

See how much posting your work helps? Good job.