Solve for x, check for any extraneous solutions.
sqrt(2x+1) -8= -5
I got x=-5 and x=4.
You apparently know how to solve equations with
square roots. You only need to learn how to check
your answers. You must always check answers in
equations containing square roots, for they often
give bogus solutions.
Let's check your first answer x=-5
That has a neative number under a square root,
so it cannot be a real number. So -5 is an
extraneous solution. So we discard it.
Let's check your second answer x=4
That one checks. So x = 4 is the only
solution.
Edwin