Could someone please help me with this problem?

square root of (2x+1) -5 = 8
I think I take the 5 and add it to the 8 and then I have
square root of (2x+1) = 13
then do I square both sides and end up with 2x+1 = 13^2
2x+1=169
2x+1-1=169-1
2x=168
x=84 am I even close on this?

The best way to check is to substitute your answer back into the equation.

SQRT(2x+1)-5=8
SQRT( (2*84)+1)-5=8
SQRT(168+1)-5=8
SQRT(169)-5=8
13 - 5 = 8
8 = 8
You are correct!

To solve the equation √(2x+1) - 5 = 8, you are on the right track, but there's a mistake in the next step.

Starting from √(2x+1) = 13, you need to square both sides of the equation to eliminate the square root. However, when squaring both sides, you must consider both the positive and negative solutions.

So, squaring √(2x+1) = 13 gives you (2x+1) = 169. However, you also need to consider the negative solution, which would be -13.

Now you can solve both equations separately:

1) (2x + 1) = 169
Subtract 1 from both sides: 2x = 168
Divide by 2: x = 84

2) (2x + 1) = -13
Subtract 1 from both sides: 2x = -14
Divide by 2: x = -7

Therefore, the solutions to the equation √(2x+1) - 5 = 8 are x = 84 and x = -7.