Question 598315
You are correct. You cannot factor {{{4x^2+5}}}. So you simply solve for x.


{{{4x^2+5=0}}}


{{{4x^2=-5}}}


{{{x^2=-5/4}}}


{{{x=""+-sqrt(-5/4)}}}


Now if you haven't learned about complex/imaginary numbers yet, then you would ignore this (and the rest of the solution) and simply say that the only solution is {{{x=-4/5}}}



However, if you have learned about complex/imaginary numbers, then...


{{{x=""+-sqrt(-5/4)}}}


{{{x=(i*sqrt(5))/2}}} or {{{x=-(i*sqrt(5))/2}}}


So if you have learned about complex/imaginary numbers, then there are three solutions and they are {{{x=-4/5}}}, {{{x=(i*sqrt(5))/2}}} or {{{x=-(i*sqrt(5))/2}}}