Question

@kayders1997


72 = 32q^2

Answer 1

I have to solve this but it needs to have two answers

Answer 2

Do you have an idea of where to start?

Answer 3

set to equal zero!

Answer 4

You don't have to in this one

Answer 5

\[0 = 32q ^{2} -72\]

Answer 6

You could isolate to get q^2 on one side

Answer 7

You could do that too and factor out the greatest common factor I suppose :)

Answer 8

Which way do you want to do it :)

Answer 9

the way that I set it up if we could please

Answer 10

Yeah we can do it that way! I can show you my way too after we're done if you would like

Answer 11

So what is the greatest common factor between the 2

Answer 12

8?

Answer 13

Yes I think that is it, so how would that look after you take that out?

Answer 14

\[0 = 8 (4q ^{2} - 9)\]
?

Answer 15

Good now you have to split up the two parts do you know how to do that?

Answer 16

Where the first part will equal 0 and the second part will equal 0

Answer 17

\[0 = 8(2q -3) (2q-3)\]

?

Answer 18

I am not entirely sure of what i'm doing

Answer 19

You don't have to factor again

Answer 20

Since we have the outside of 8 we can set that equal to 0 so 8=0 is that true though?

Answer 21

no

Answer 22

good, now we can set the other part equal to 0 so 4q^2-9=0 the reason why we can do this is because we have the outside part the part where you factored something out and an inside part

Answer 23

So 4q^2-9=0 do you know how to do this part?

Answer 24

sooo just ignore the 8?

Answer 25

Yes because 8 does not equal 0

Answer 26

alright. moving on then.

\[4q ^{2}=9\]

Is that the next step?

Answer 27

Yes good

Answer 28

Now do you know what's next? :)

Answer 29

something having to do with perfect squares right?

Answer 30

You don't have to do that think of PEMDAS backwards we just want q^2=some number

Answer 31

so division

Answer 32

good yes :) so you get?

Answer 33

\[q^{2} = \frac{ 9 }{ 4 }\]
Is that the answer?

Answer 34

Almost!!!

Answer 35

it doesn't seem quite right...

Answer 36

But that is the correct step

Answer 37

Now how do you undo something that is being squared?

Answer 38

I know what it is but I can't for the life of me remember what it's called.

Answer 39

OH WAIT

Answer 40

THE ROOT

Answer 41

:)

Answer 42

IS IT THE ROOT

Answer 43

Yes square root

Answer 44

So...you get!!!!! :)

Answer 45

q= \[q = \frac{ 3 }{ 2 }\]

Answer 46

Yes :) and remember when you take the square root you get a plus minus answer so it is q=+3/2 and q=-3/2 and we could check that by putting those back into the equation

Answer 47

Do you wanna see the way I approached it?

Answer 48

wait a second. break that last bit down again please? it can be a positive or negative answer right? so in order to find out you have to send the fraction through what equation to see if the fraction (not the individual numbers) is + or - ?

Answer 49

brb getting food

Answer 50

back

Answer 51

Okay so when you take the square root you will always get a + answer and a - answer, it's just a rule like if you think about the graph x^2 where is two x values when the y value is 1 x=1 and x=-1 that's why, because this is an even function so it will have the same look on both sides of the graph, and than the second part we can plug in the x values back into the function 72=32q^2 so we got -3/2 so let's plug that in 72=32(-3/2)^2 when you do the (-3/2)^2 you get 2.25 and than times that by 32 you get 72 and 72=72 if you do that with the positive answer so put in 3/2 so 72=32(3/2)^2 so again you do the (3/2)^2 and you got 2.25 multiply that by 32 72=72 so that's how you can check the answers

Answer 52

if it's the same both ways do you write the answer like this:

\[q = \pm \frac{ 3 }{ 2 }\]

Answer 53

Yes you can

Answer 54

Or you can write it separate doesn't matter they are both correct :)

Answer 55

Do you want to see my way, it is quicker if you don't that's okay too :)

Answer 56

yeah! (i may or may not understand... just a warning)

Answer 57

That's okay I'all try to explain step by step as best as I can

Answer 58

72=32q^2 first I know we wanted to solve for q so first I divided by 32 so you would only have q^2 on the one side so you would get q^2=9/4 does that make sense?

Answer 59

suprisingly...yes

Answer 60

And than we just took the root like we did before and we get q=+3/2 and q=-3/2

Answer 61

Does that make sense? :)

Answer 62

yeah. I can't believe my teacher doesn't use this method in class

Answer 63

Really? Omg!!! It's super quick, and in my mind pretty easy, factoring works too as we just seen, but yes there is more than one way to solve problems like these :)

Answer 64

weird. did i mention that we use a common core A1 book? that might have something to do with her not using this.

Answer 65

Yes you have, I don't think it should matter though I want to become a math teacher myself, but I haven't gotten to things like common core standards for classes, I'm not even in college yet :D

Answer 66

But I wouldn't think it would matter this is a way to solve an equation for a variable which has to be a common core standard in an algebra book