How do you solve #n^ { 2} - 20n - 96= 0#?

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Answer 1 · 2018-01-08T21:43:21

Factorise and then solve by setting the brackets = to 0.

See below.

To solve a quadratic we know that we must get factors of #c# that add/ subtract to give #b#

#therefore# we need factors of #-96# that add/ subtract to give #-20#

After playing around with the numbers you should find that #-24# and #4# work perfectly.

#therefore n^2-20n-6=0#
is the same as #(n-24)(n+4)=0#

We know that a quadratic will always #=0#, meaning one of our brackets must = 0.

#therefore (n-24)(n+4) = 0#

#n=24 , n=-4#