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

Kaydence Huff

Kaydence Huff

Answered question

2022-01-21

How do solve n210n+22=2?

Answer & Explanation

Brynn Ortiz

Brynn Ortiz

Beginner2022-01-22Added 12 answers

n210n+22=2
is equivalent to
n210n+24=0
We would like to factor the left hand size to get something of the form
(n+a)(n+b)=n210n+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
(n6)(n4)=n210n+24=0
which implies that n=6 or n=4

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