savvers Group Title -4sqrt(x+9)=20 can anyone help? 2 years ago 2 years ago

1. geoffb

$-4 \sqrt{(x+9)} = 20$ Like this? At what part are you getting stuck?

2. savvers

well i get x=16 but when i try to see if its true i get -20=20

3. savvers

and yes like that

4. geoffb

Yeah, with that -4 outside the square root, I think it's undefined.

5. savvers

yeah your probably right. extraneous solution?

6. geoffb

If we defined $$y$$ as $$\sqrt{(x+9)}$$, we would get $$-4y = 20$$, with $$y = -5$$, and there is no way $$\sqrt{(x+9)} = -5$$

7. savvers

hmmm i dont know. but when we divide -4 we get $\sqrt{x+9}=-5$

8. geoffb

$$\large{\sqrt{-x} = i \sqrt{x}}$$ right?

9. savvers

yeah

10. geoffb

Okay, can we use that somehow?

11. geoffb

Oh wait... We can square both sides, right?

12. savvers

hmmm yeah

13. savvers

and we get x+9=25 because -5x-5=25

14. geoffb

Right, so you were right with 16; it is an extraneous root.

15. savvers

yeah it looks like that then and thanks man

16. geoffb

Hey, no problem. :)