Solving for XDate: 5/14/96 at 23:44:24 From: Tanya Chongchit Subject: X^2 - 7X + 10 = 0 I am having a totally hard time trying to figure out this equation and it is getting on my nerves! Please help me and show me each step to solving X. Thank you! X^2 - 7X + 10 = 0 Is this what I am supposed to do? (X-5)(X-2) Then is the answer X = 5 and X = 2? Thank you again! Tanya Date: 5/16/96 at 19:41:14 From: Doctor Syd Subject: Re: X^2 - 7X + 10 = 0 Hey! We're glad you wrote. Sometimes it can certainly be frustrating when you don't think you know how to do a problem, I know! But, hey, you got this problem! Do you understand why and how you factored the polynomial? You were hoping that x^2 - 7x + 10 would factor into something nice, in the form (x + a)(x + b) where a and b are integers, right? Well, how do you figure out what a and b are? Let's expand the product: (x + a)(x + b) = x^2 + (a+b)x + ab We want to find out for what values of a and b we have that (x + a)(x + b) = x^2 + (a-b)x + ab = x^2 -7x + 10 This means that we must have a-b = -7 and ab = 10. You have two equations now and two unknowns. You can either solve for a and b algebraically or you can try some numbers until you find some that work. You can see that a = -5 and b = -2 work, and thus you can say with confidence that (x-2)(x-5)=x^2 - 7x +10 If this product is equal to 0, then one of the terms in the product is zero. In other words, either x-2 = 0 or x-5 =0. Solving for x, this means that either x = 2 or x = 5. Thus we have found the solution to the equation. You had all of the right steps...I just filled in an explanation. I hope this helps! Good luck with other problems like this. Once you've practice a little it will all seem much easier, I promise! -Doctor Syd, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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