Question

What is the solution of 3sqrt(x+8=-4

Answer 1

Hello there!


`3 √(x+8)=-4`

So this is the equation we have, and I'm guessing we have to solve for the value of x.

Let's divide both sides by 3.


`√(x+8)=-4/3`

Square both sides to get rid of the square root.


`x+8=(-4/3)^2`

`x+8=16/9`

Subtract both sides by 8.


`x=16/9-8=16/9-72/9=-56/9`

`x=-56/9`

Let’s test if this is an extraneous solution by plugging this value into the equation.


`3 √(-56/9+8)`

`=4`

This does not produce the desired result, which was supposed to be -4. Thus, x=-56/9 is an extraneous solution, so there are no solutions to this equation.

I hope this helps and have an awesome day! :)
~AgentCozmo4, Moderator

Answer 2

Solve for x:
3 sqrt(x + 8) = -4

Divide both sides by 3:
sqrt(x + 8) = -4/3

Raise both sides to the power of two:
x + 8 = 16/9

Subtract 8 from both sides:
x = -56/9

3 sqrt(x + 8) ⇒ 3 sqrt(8 - 56/9) = 4:
So this solution is incorrect

The solution is incorrect:
Answer: (no solutions)