## anonymous 3 years ago Solve for x?

1. anonymous

$-4\sqrt{x+9}=20$

2. anonymous

sqrt(x+9)=-(20/4)

3. anonymous

I know how to solve is, I'm just not sure how to get rid of the -4 in the front of the radical.

4. anonymous

you need to remove the square from x+9 the way you do that is by squaring both side and you end up with x+9=-(20/4)^2. then solve from there.

5. anonymous

yes that 's it

6. anonymous

x+9=-20/4)^2. -20/4^2 = -25 then take -25 subtract 9. you will get the answer of x=-34

7. anonymous

it's easy to see that this has NO SOLUTION: (-4)*(-5) = 20 so that means: $$\large -4\sqrt{x+9}=20 \rightarrow \sqrt{x+9}=-5$$ $$\large \sqrt{x+9}=-5$$ which has no solution because the left side is always positive but the right side is negative

8. anonymous

Can't you just square both sides to get rid of the square root, then solve like an equation?

9. anonymous

yes you can try to do that... it's one technique you should try to solve it. but why continue when you know this is an impossible equation to solve?

10. anonymous

not impossible, no solution... if you do solve it, the solution is an extraneous solution....

11. anonymous

If according to your answer it is √x+9 = -5 then you'd square both sides to have: x+9 = -25 subtract 9 from both sides and get -16 as x?

12. anonymous

Difficult equation in history

13. anonymous

squaring both sides you get positive 25

14. anonymous

Oh, that's right thanks so then x+9=25 subtract 9 then positive 16?

15. anonymous

yes... now let's see if the solution of x=16 works....

16. anonymous

no no no no =-20

17. anonymous

that's wrong

18. anonymous

$$\large (-4)(\sqrt{x+9})=20$$ $$\large (-4)(\sqrt{\color {red}{16}+9})=20$$ $$\large (-4)(\sqrt{\color {red}{25}})=20$$ $$\large -4 \cdot 5 = 20$$ $$\large -20=20$$ ???? not a true statement

19. anonymous

so the solution of x=16 is extraneous and not really a solution.

20. anonymous

solution $\left| -4 \right|$

21. anonymous

suggestion hhhh

22. anonymous

@AntarAzri , what's the solution?

23. anonymous

$\left| -4 \right|$

24. anonymous

$$\large (-4)(\sqrt{x+9})=20$$ $$\large (-4)(\sqrt{|-4|+9})=20$$ $$\large (-4)(\sqrt{4+9})=20$$ $$\large (-4)(\sqrt{13})=20$$ x=|-4| doesn't seem to work. That's not a solution.

25. anonymous

my oh my I have headaches because of this problem..

26. anonymous

no no i dont mean the x |−4|=4

27. anonymous

ok. whatever... my answer stands... NO SOLUTION to the equation: $$\large (-4)(\sqrt{x+9})=20$$ \)

28. anonymous

$(\left| -4 \right|)(\sqrt{16+9})=20$

29. anonymous

here's wolframs answer: http://www.wolframalpha.com/input/?i=solve+-4*sqrt%28x%2B9%29%3D20

30. anonymous

good

31. anonymous

http://www.wolframalpha.com/input/?i=solve+ |%E2%88%924|*sqrt%28x%2B9%29%3D20

32. anonymous

?

33. anonymous

if u don't understand my answer and expanation maybe someone else can give u a better answer... i will not argue my point further....

34. anonymous

Do we agree that it can not be the root of a negative number gives a positive number ?

35. anonymous

I'll see what my teacher says when she grades it. Thanks for your time