Question

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

Answer 1

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)

Answer 2

Hello there!

$3 \sqrt{x+8}=-4$

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.

$\sqrt{x+8}=-4/3$

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.

$3 \sqrt{-56/9+8}$
$=4$

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