FactoringDate: 9/5/95 at 0:1:30 From: Anonymous Subject: algebra Question: How do I solve x^2+x-12=0 ? Date: 9/6/95 at 12:11:50 From: Doctor Ken Subject: Re: algebra Hello! The way that most people like to solve problems like this is to FACTOR the expression x^2 + x - 12. I'll do an example that's similar to yours, then see whether you can do your problem. I'll do x^2 + x - 30 = 0. First figure out all the ways you can factor 30 as the product of two numbers: 1 x 30 2 x 15 3 x 10 5 x 6 Then, since we're going to have something in the form of (x - one factor)(x + the other factor), we use this to decide which of the pairs of factors we should use. At this point, it's kind of guess-and-check. The key here is that we're looking for factors that have a difference of 1. That's because the coefficent on the x term is 1. So looking down the list, it looks like 5 x 6 will work. Should we use (x - 5)(x + 6), or (x - 6)(x + 5)? Well, the first one gives us x^2 + x - 30, and the second gives us x^2 - x - 30. So we use the first one. Once we have that, we know that x is either 5 or -6. Do you see how you might do you your problem now? Factoring is something that really takes a lot of practice to get good at. - Doctor Ken, The Geometry Forum |
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