Examining the equation
We have 2 terms:
[tex]\sqrt{x+2}[/tex] and [tex]\sqrt{4x+1}[/tex]
For the sum of these to equal a negative number, in this case -3, one of these terms would have to be negative.
So what's the problem?
The function [tex]\sqrt{x}[/tex] (square root of x) only returns positive values!
(See the attached image for a graph of [tex]\sqrt{x}[/tex])
Since neither of the terms can be negative, it can't be equal to -3. In other words, no matter what we put as [tex]x[/tex], we can't solve the solution, so we say that the equation does not have any solutions.
