Question

How do you solve `sqrt(4x+1)+3=0`?

Answer 1

You can't.

Explanation:

`sqrt(4x+1)+3=0`

Subtract `-3` from both sides,

`sqrt(4x+1)=-3`

Since the square root of any number cannot be negative, there are no values of `x` that satisfies the equation.

Answer 2

Actually, there is no solution.

Explanation:

I know everyone else said that the solution is `x=2`, but if you plug it in, it doesn't hold up:

`color(white)=>sqrt(4x+1)+3=0`

`=>sqrt(4(2)+1)+3=0`

`color(white)=>sqrt(8+1)+3=0`

`color(white)=>sqrt(9)+3=0`

`color(white)=>3+3=0`

`color(white)=>6!=0`

You can also look at the graph of `sqrt(4x+1)+3` and see that there are no zeroes:

graph{sqrt(4x+1)+3 [-10.24, 15.07, -3.37, 9.29]}

Here's the flaw in trying to solve it:

`sqrt(4x+1)+3=0`

`sqrt(4x+1)=-3`
`" "color(red)uarr`
Here's the mistake. A square root cannot equal a negative number, so the process needs to stop here. Unfortunately, you can't square both sides.

Hope this helped!