## anonymous one year ago What is the solution of the equation? 2 5^square root (x+6)^3+3=19

1. anonymous

not so easy to read this one $25\sqrt{x+6}^3+3=19$?

2. anonymous

$2 \sqrt[5]{(x+6)^{3}} +3 =19$

3. misty1212

HI!!

4. misty1212

fifth root right?

5. anonymous

2^5 sqrt((x+6)^3) + 3 = 19 32 sqrt ((x+6)^3) = 16 sqrt ((x+6)^3) = 0.5 (x+6)^3 = 0.25 x+6 = 0.6299605249 x = -5.3700394751 The answer is nothing.

6. misty1212

first subtract 3 from both sides

7. anonymous

@satellite73

8. anonymous

what @misty1212 said, subtract 3 as a first step what do you get?

9. anonymous

Answer choices are A.26 C.14 D.2

10. anonymous

A

11. anonymous

yeah yeah we can get the answer subtract 3 and get $2\sqrt[5]{x+6}=16$ then divide both sides by $$2$$

12. anonymous

Subtract from 19 or from the whole equation itself?

13. anonymous

from both sides your goal is to get $$\sqrt[5]{x+6}$$ by itself

14. anonymous

16/2=8

15. anonymous

just like if you were solving $2x+3=19$ for $$x$$ you would a) subtract 3 then b) divide by 2

16. anonymous

idk how to divide the other side

17. anonymous

right

18. anonymous

you have it $\sqrt[5]{x+6}^3=8$

19. anonymous

now to get $$x$$

20. anonymous

I just dont know what to do with the left side lol

21. anonymous

I appreciate you taking your time to help me btw

22. anonymous

lets start with $\sqrt[5]{(x+6})^3=8$

23. anonymous

getting there was the first two steps, you good til here (yw btw)

24. anonymous

$\sqrt[5]{(x+6})^{\color{red}3}=8$ lets get rid of that $$\color{red}3$$ next it is an exponent, so to get rid of it, take the cubed root of both sides you know what the cubed root of 8 is?

25. anonymous

I have no clue

26. anonymous

think of a number that, when you multiply it by itself 3 times, you get 8 just guess, you have very few choices if you get it wrong, i will tell you

27. anonymous

2

28. anonymous

right!

29. anonymous

so taking the cubed root of both sides gets rid of that exponent of 3 on the left and $\sqrt[5]{(x+6)^3}=8$ becomes $\sqrt[5]{x+6}=2$

30. anonymous

now we have to get rid of the index of 5, which we do by raising both sides to the power of 5 what is $$2^5$$?

31. anonymous

you can back solve it

32. anonymous

i didn't lose you there did it?

33. anonymous

Sorry catching up my computer froze

34. anonymous

yeah it does that

35. anonymous

os i mean

36. anonymous

just put all the options one by one in the question and one option will satisfy the equation

37. anonymous

raisiing both sides to the power of 5 gives $x+6=2^5$ or $x+6=32$

38. anonymous

32

39. anonymous

right

40. anonymous

now subtract 6 from both sides and you are done

41. anonymous

32-6

42. anonymous

yup

43. anonymous

26

44. anonymous

yes

45. anonymous

Wow thank you, I would have never figured that out without you breaking it down

46. anonymous

you are quite welcome

47. anonymous

I gave you a medal, well deserved

48. anonymous

I was right the answer is 26

49. anonymous

You were right, but you just gave the answer instead of explaining lol that wont help me on a test

50. anonymous

i prefer quick learning

51. anonymous

as like in mcq's u have to save time....not to write papers for one question only