Pre algebra
posted by Grace .
How do I solve Quadratic equations by factoring?
(for example how would I solve n2  10n = 21 if I was supposed to get the answers 7 and 3?

first, set everything equal to zero.
n^2  10n + 21 = 0
now, since (na)(nb) = n^2  (a+b)n + ab, we are looking for two numbers a and b, which multiply to 21 and add to 10.
Now, the only factor of 21 are 7 and 3. Luckily, they add to 10, so we have
(n7)(n3) = n^2  10n + 21
Now, back to step 1. Why set everything to zero? We now have
(n7)(n3) = 0
the only way two numbers can multiply to zero is if one or the other of them is zero. So, we have either
n7 = 0 ==> n=7
or
n3 = 0 ==> n=3
Those are the solutions to
(n7)(n3) = 0, which is just a rewriting of the original equation.
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