How do solve #n^2 - 10n + 22 = -2#?

1 Answer
Alan P.
Mar 28, 2015

#n^2-10n+22= -2#
is equivalent to
#n^2-10n+24=0#

We would like to factor the left hand size to get something of the form
#(n+a)(n+b) = n^2-10n+24#

Since the final term is positive, #a# and #b# must have the same sign
and
since the coefficient of #x# is negative they must both be negative.

So we are looking for negative values #a# and #b# such that
#a+b = -10#
and
#ab = +24#

Assuming integer solutions there are very few possibilities.
By trial and error we can derive
#(n-6)(n-4) = n^2-10n+24 = 0#

which implies that
#n=6# or #n=4#

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