How do you solve the quadratic 8n^2-5=-110 using any method?

1 Answer
Alan P.
Dec 29, 2016

No Real solutions are possible for the given equation.
Complex solutions: +-isqrt(105/8)

Explanation:

Real Solutions
8n^2-5=-110color(white)("XX")rarrcolor(white)("XX")8n^2=-105
but 8 > 0 and n^2 >=0 for all Real values of n
so 8n^2 >= 0 and can not be equal to a value less than 0

Complex Solutions
8n^2=-105color(white)("XX")rarrcolor(white)("XX")n^2=-105/8

n^2=105/8 * i^2 color(white)("XXX")rarrcolor(white)("XXX")n=+-(sqrt(105/8)) i
...alternately, you could apply the quadratic formula to 8n^2+0n+105=0 (and get the same result).

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