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Q: Solving quadratic equations by Factoring ( Answered,   4 Comments )
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
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
(click to see it)
the quadratic formula is
(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

[square root of](b*b - 4 * a * c)
described here:

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

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!
Subject: Re: Solving quadratic equations by Factoring
From: redhoss-ga on 23 Aug 2006 19:49 PDT
Too bad the problem isn't x^2+5x-14=0
Subject: Re: Solving quadratic equations by Factoring
From: xaviergisz-ga on 23 Aug 2006 21:12 PDT
too bad it's not x^2+7x+14=0
Subject: Re: Solving quadratic equations by Factoring
From: xaviergisz-ga on 23 Aug 2006 21:15 PDT
oops, ignore that comment :P
Subject: Re: Solving quadratic equations by Factoring
From: thither-ga on 23 Aug 2006 21:50 PDT
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:

   This method is generalized in the form of the quadratic formula,
which I imagine will be your son's next topic:

   I hope this helps.

   Have a good day.

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