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

- anonymous

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

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- anonymous

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

- anonymous

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

- misty1212

HI!!

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## More answers

- misty1212

fifth root right?

- 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.

- misty1212

first subtract 3 from both sides

- anonymous

@satellite73

- anonymous

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

- anonymous

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

- anonymous

A

- anonymous

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

- anonymous

Subtract from 19 or from the whole equation itself?

- anonymous

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

- anonymous

16/2=8

- anonymous

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

- anonymous

idk how to divide the other side

- anonymous

right

- anonymous

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

- anonymous

now to get \(x\)

- anonymous

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

- anonymous

I appreciate you taking your time to help me btw

- anonymous

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

- anonymous

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

- 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?

- anonymous

I have no clue

- 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

- anonymous

2

- anonymous

right!

- 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 \[\sqrt[5]{x+6}=2\]

- 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 \(2^5\)?

- anonymous

you can back solve it

- anonymous

i didn't lose you there did it?

- anonymous

Sorry catching up my computer froze

- anonymous

yeah it does that

- anonymous

os i mean

- anonymous

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

- anonymous

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

- anonymous

32

- anonymous

right

- anonymous

now subtract 6 from both sides and you are done

- anonymous

32-6

- anonymous

yup

- anonymous

26

- anonymous

yes

- anonymous

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

- anonymous

you are quite welcome

- anonymous

I gave you a medal, well deserved

- anonymous

I was right the answer is 26

- anonymous

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

- anonymous

i prefer quick learning

- anonymous

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

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