8x-3(3x-2)=1

I liked math, and I used to be able to rock these kind of equations. But it appears that in my old age, memories of the Hallowe'en party in 1999 have pushed out how to solve for x. Here's what I have so far:

- First, we multiply everything inside the brackets with everything outside the brackets:
- 24x
^{2}-16x-9x+6=1 - So, now we group stuff and add other stuff together:
- 24x
^{2}-25x=-5 (because if you subtract the 6 from one side, you have to do it to the other side as well.) - Here's where I start forgetting things. I want to get rid of the x's, right? So I divide both sides by x, correct? Thus, I have:
- 24x-25=-5/x (Yeah, I skipped some work, but I was getting tired of writing the tags to make the "2" superscript)
- I left the scrap of paper I was using to work on this at work, but do I put all the x's on one side now, and put the -25 on the other?
- 24x+5/x=25

(Update: I am an idiot. As Jen very helpfully pointed out, I got it wrong. Oh so wrong. I was trying to solve the equation as a quadratic equation, but it quite obviously isn't. For those of you playing along at home, a quadratic equation would have had both sets of numbers in brackets.

As Lise, fellow Dal grad, book clubber and Librarian at Laurentian wrote me this afternoon:

Oh! Oh! Pick me, pick me!

If you actually did mean 8x - 3(3x-2) = 1, then your question is much

simpler: it becomes 8x - [9x -6] = 1; 8x-9x+6=1; -1x = -5; therefore x = 5.

But if you did mean to write (8x-3)(3x-2)=1, you're dealing with a

quadratic equation, and you'll have two possible answers for x (your

thought of trying to solve for x makes perfect sense, but there's a

different way of approaching it when you have x^2 and x in the same equation). Your first step is to solve for 0, so (I won't write the steps - I know you can do this part) you get 24x^2 -25x +5 = 0, and ideally you could factor it at this point, but this particular equation doesn't factor nicely with integers. So for this equation you can find the solution by the dreaded completing the square method. You'll end up with x = (25/48) +/- sqrt(145/2304); therefore x =0.77 or x=0.27. Not very pretty, but it works.

God, I amsucha math geek. I was way too excited about this.

You guys are the best! Thanks! I owe you both a beverage of your choice :)