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

↳Redirected from "What polyatomic ion has a positive charge?"
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).

Related questions
See all questions in Completing the Square
Impact of this question
2220 views around the world
You can reuse this answer
Creative Commons License