## vivalakoda 3 years ago Solve for x?

1. vivalakoda

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

2. AntarAzri

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

3. vivalakoda

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

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. AntarAzri

yes that 's it

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

7. dpaInc

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. vivalakoda

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

9. dpaInc

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. dpaInc

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

11. vivalakoda

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. AntarAzri

Difficult equation in history

13. dpaInc

squaring both sides you get positive 25

14. vivalakoda

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

15. dpaInc

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

16. AntarAzri

no no no no =-20

17. AntarAzri

that's wrong

18. dpaInc

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

19. dpaInc

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

20. AntarAzri

solution $\left| -4 \right|$

21. AntarAzri

suggestion hhhh

22. dpaInc

@AntarAzri , what's the solution?

23. AntarAzri

$\left| -4 \right|$

24. dpaInc

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

25. vivalakoda

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

26. AntarAzri

no no i dont mean the x |−4|=4

27. dpaInc

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

28. AntarAzri

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

29. dpaInc

30. AntarAzri

good

31. AntarAzri

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

32. vivalakoda

?

33. dpaInc

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. AntarAzri

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

35. vivalakoda

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