College Algebra Problem

[ECHOSIDE]

Is the number 4 a solution to √(3x+4)=-4?

I say yes, my math book says no. Here's my logic:

Finding the domain of x:
3x+4≥0
3x≥-4
x≥-(4/3)

Domain of x: [-(4/3), ∞)

√(3x+4)=-4
√(3(4)+4)=-4
√(12+4)=-4
√16=-4
-4=-4 or 4=-4
4=-4 is thrown out
-4=-4 is true, therefore x=4 is a solution to the original equation.

I appear to be misunderstanding something here. I'm sure it's simple. Can you provide any assistance?

Thanks!

 

[clarkjd]

1 square both sides of the equation to remove the radical:
3x+4 = 16
3x =16-4
3x=12
x=4

 

[dogman_1234]

So, the answer is 2?

 

[ECHOSIDE]

Thank you, clarkjd, for your thoughtful response.
Dogman_1234, I'm sorry to inform you that the answer is not 2.
What must be considered here is the range of the square root operation. I did not understand that the square root symbol implies that the radical is to be solved only for the principal square root. This means that the range of the radical, when solved, is [0, ∞). No input value, x, will produce an output of -4. Therefore, x=4 is not a solution.

 

[dogman_1234]

Oh, okay.

Makes sense. 😀