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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