## vivalakoda Group Title Solve for x? one year ago one year ago

1. vivalakoda Group Title

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

2. AntarAzri Group Title

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

3. vivalakoda Group Title

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 Group Title

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 Group Title

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 Group Title

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

9. dpaInc Group Title

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 Group Title

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

11. vivalakoda Group Title

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 Group Title

Difficult equation in history

13. dpaInc Group Title

squaring both sides you get positive 25

14. vivalakoda Group Title

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

15. dpaInc Group Title

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

16. AntarAzri Group Title

no no no no =-20

17. AntarAzri Group Title

that's wrong

18. dpaInc Group Title

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

19. dpaInc Group Title

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

20. AntarAzri Group Title

solution $\left| -4 \right|$

21. AntarAzri Group Title

suggestion hhhh

22. dpaInc Group Title

@AntarAzri , what's the solution?

23. AntarAzri Group Title

$\left| -4 \right|$

24. dpaInc Group Title

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

25. vivalakoda Group Title

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

26. AntarAzri Group Title

no no i dont mean the x |−4|=4

27. dpaInc Group Title

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

28. AntarAzri Group Title

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

29. dpaInc Group Title

30. AntarAzri Group Title

good

31. AntarAzri Group Title

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

32. vivalakoda Group Title

?

33. dpaInc Group Title

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 Group Title

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

35. vivalakoda Group Title

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