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.

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.