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 Subject: Solving quadratic equations by Factoring Category: Reference, Education and News > Homework Help Asked by: goobygoo-ga List Price: \$2.00 Posted: 23 Aug 2006 18:42 PDT Expires: 22 Sep 2006 18:42 PDT Question ID: 758939
 ```My son (in algebra 2) was given a homework assignment to solve the following by FACTORING (ONLY!) and WITHOUT the use of a calculator. x^2+7x-14=0. I don't see how this can be done without using a calculator. Would someone please give me a walkthrough on how to do this.```
 Subject: Re: Solving quadratic equations by Factoring Answered By: richard-ga on 25 Aug 2006 19:26 PDT
 ```Hello and thank you for your question. The equation cannot be solved by ordinary factoring, because the factors are not whole numbers. There's an algebraic formula, called the quadratic formula, that solves quadratic equations of the form http://id.mind.net/~zona/mmts/miscellaneousMath/quadraticFormula/qexp0.gif (click to see it) the quadratic formula is http://id.mind.net/~zona/mmts/miscellaneousMath/quadraticFormula/qesol0.gif (click to see it) I understand you're not permitted to use the formula-- I mention it here because it includes a mathematicl sequence called the discriminant: [square root of](b*b - 4 * a * c) described here: http://www.mathwords.com/d/discriminant_quadratic.htm So in your problem the discriminant is: [square root of] 7*7 -(4*1*(-14) or [square root of]49 + 56 and that's 10.2469508 ://www.google.com/search?hl=en&lr=&rls=GGLG%2CGGLG%3A2006-16%2CGGLG%3Aen&q=%28105%29%5E.5 So since that number is part of the answer, he's not going to find it by factoring! [a comment below is correct in saying you can find the answer by 'completing the square' which is a sort of factoring, but if your son hasn't been taught that method I'm sure they don't expect him to invent that method by himself] Search terms used: quadratic formula Thanks again for letting us help! Richard-ga```
 `Too bad the problem isn't x^2+5x-14=0`
 `too bad it's not x^2+7x+14=0`
 `oops, ignore that comment :P`
 ```The equation can be solved by the method of "completing the square". If you search this phrase you'll find many sites which explain how its done. Here is one: http://www.sosmath.com/algebra/quadraticeq/complsquare/complsquare.html This method is generalized in the form of the quadratic formula, which I imagine will be your son's next topic: http://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html I hope this helps. Have a good day.```