I'm trying to solve the inequality 25x^2+16<40x.
I first rearrange the inequality to 25x^2-40x+16<0
Then I factor, resulting in (5x-4)^2<0
But here is where I get confused. I know the answer is that there are no real solutions, but I seem to be able to get x<4/5. Why is this inequality one with no solution?
no matter what real value x has, this expression will be some real number squared.
When you square ANY real number the outcome CANNOT be NEGATIVE.
So thee is no way that this expression can be less than 0.
If x=4/5 then the expression will be 0
Consider if x=0 (which is less than 4/5)
(5*0-4)^2 = (-4)^2 = 16 which is definitely not less than 0.