Question

Find the solution of 3 times the square root of the quantity of x plus 6 equals negative 12, and determine if it is an extraneous solution.

Answer 1

@ospreytriple @BloomLocke367 @freckles

Answer 2

First off, can you write that in an equation?

Answer 3

yes

Answer 4

Do that first. Tell us what you get.

Answer 5

You have\[3\sqrt{x+6} = -12\]What do you think we should do first?

Answer 6

\[3\sqrt{x+6}=-12\]

Answer 7

not sure

Answer 8

There are a few ways to do this, but the easiest would be to isolate the radical. Do you know how you would do that?

Answer 9

Well we have to get the 'x' stuff all by itself, so how would you get rid of that 3?

Answer 10

square it?

Answer 11

you have to get rid of the 3 first. Right now, the 3 is being multiplied with \(\sqrt{x+6}\). How do you "get rid of" something that is being multiplied?

Answer 12

divide

Answer 13

Yes! now divide both sides by 3 and tell me what you're left with

Answer 14

i don't have a calulator with me right now

Answer 15

You don't know \(-12\div 3\)?

Answer 16

yes its -4

Answer 17

There you go. so right now, you have \(\sqrt{x+6}=-4\) correct?

Answer 18

yes

Answer 19

Now, how would you get rid of that radical?

Answer 20

hmm im not sure

Answer 21

Well, what's the opposite of taking the square root of something?

Answer 22

squaring it?

Answer 23

im clueless on this sorry

Answer 24

yes! so you have to square both sides :D

Answer 25

Don't apologize. You're doing great :D

Answer 26

okay, thanks!

Answer 27

so it would be x^2+36=16?

Answer 28

No, because when you squared it, it just cancelled out the radical. For instance, when you take \(\sqrt1^2\), you don't get \(1^2\) do you? No, you just get 1. Try again. The right side is correct.

Answer 29

so, x+6=16?

Answer 30

Yep!

Answer 31

ok, thanks! so then it would be x=10 right?

Answer 32

and would it be extraneous or not extraneous though?

Answer 33

mhm, I'm pretty certain. Let me ask @Nnesha if I did this correctly. Now we just have to check to make sure it's not extraneous. Do you know what an extraneous solution is?

Answer 34

did a great job!

Answer 35

Okay, thanks. lol

@iwanttogotostanford do you know what an extraneous solution is?

Answer 36

@BloomLocke367 yes

Answer 37

Then graph it and find out if there's a point where x=4

Answer 38

do you know if it is or not? I'm sorry I'm just in a very hard place right now to be graphing things (I'm on a plane)

Answer 39

you can substitute x for 10 into the original equation to find out if it's extraneous or not. :=)

Answer 40

thanks! @Nnesha

Answer 41

Sorry, I was afk. Thanks @Nnesha

Answer 42

np

Answer 43

if you get equal sides then it's not extraneous
if both sides are not equal then 10 would be an extraneous

Answer 44

ok thanks do u know if it is or not? @Nnesha

Answer 45

oops, I don't know why I said 4 earlier, I meant to say 10. lol

Answer 46

no i don't. you have to figure it out!

Answer 47

@Nnesha well i don't have paper with me so its really hard

Answer 48

welll, you can use `paint`

Answer 49

that would be fun! trust me

Answer 50

ok, thank you @Nnesha

Answer 51

i got extraneous:-)

Answer 52

both sides are equal ?

Answer 53

no they aren't equal

Answer 54

There you go!

Answer 55

thanks!

Answer 56

o^_^o

Answer 57

they aren't equal= not extraneous?

Answer 58

You were correct the first time, it is extraneous because they are not equal.

Answer 59

wait....

Answer 60

both sides are not equal = extraneous
both sides are equal = non-extraneous

Answer 61

when you take the square root of something, it could be positive or negative

Answer 62

Right @Nnesha?

Answer 63

`something`
if you mean
square root of negative number then you will get `imaginary` solution
if you take square root of positive then you would always get positive answer

Answer 64

i think its non-extraneous

Answer 65

how so? because -4*-4=16 AND 4*4=16

Answer 66

oh whoops i did -4 times 4

Answer 67

\[\huge\rm 3\sqrt{10+16}=-12\]
whet did you get at left side ?

Answer 68

i get it now

Answer 69

I gotta go, sorry!

Answer 70

i said `number`
if -4 times -4 = positive number so square root would be positive

Answer 71

so it's extraneous or non-extraneous ?

Answer 72

ok it is extraeous then

Answer 73

yes right \[12\cancel{=}-12\]

Answer 74

thank you @Nnesha

Answer 75

np