The given equation involves a power of the variable. Find all real solutions of the equation.
x^2=24

- anonymous

The given equation involves a power of the variable. Find all real solutions of the equation.
x^2=24

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- myininaya

x=+ or - 24^(1/2)

- myininaya

x=+ or -2*6^(1/2)

- myininaya

x=2*6^(1/2)
x=-2*6^(1/2)

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## More answers

- anonymous

second one is correct. how do you come to that? it seems as if it's something really simple and i am not connecting it... can you explain?

- anonymous

i really need help figuring it out, not just the answer.

- myininaya

\[x^{2}=9\]
wouldn't you agree x=-3 and x=3
since (-3)^2=9
and (3)^2=9

- myininaya

?

- anonymous

no

- anonymous

x^2=24

- myininaya

what is (-3)^2?

- anonymous

-9

- myininaya

no (-3)^2=(-3)(-3)=9

- myininaya

-3^2=-3*3=9 since the square is only on the 3 and not the whole thing

- anonymous

i don't understand where the 3 comes from.........

- myininaya

x^2=9
just tell what would go in the place of x

- myininaya

tell me what you think would go there?
ask yourself what is something square that will give me 9?

- anonymous

i understand. maybe i don't know where you get the 9 then....

- myininaya

?
i made up the problem

- anonymous

oh. wtf... lol. i can figure out your problem, why can't i figure out this other one?

- myininaya

the 9 just came from somewhere in my head
i'm trying to show you something so you understand problems like this

- myininaya

lol

- anonymous

thanks for the example btw :)

- myininaya

x^2=9
to solve equations like this you take the square of both sides
and you always put + or -

- myininaya

the reason is, because as you seen above there are two numbers we can plug into x^2=9
that would be correct
just like if we had x^2=25
x=-5 and 5

- myininaya

x^2=81
what will your solutions be?

- anonymous

okay. that makes sense... with your example. i'm guessing because it's very simple is why i can understand it. lol

- anonymous

x=+or-9

- myininaya

you don't like it when the other side isn't a perfect square but its just like these other ones that are you can't get an integer answer though
RIGHT! :)

- myininaya

x^2=56
what would x be?

- anonymous

somewhere between 7 and 8.... :/

- myininaya

lol
x=+sqrt(56)
x=-sqrt(56)

- anonymous

okay. i can write it like that :)

- myininaya

you can simplify this
x=+ or - sqrt(8*7)=plus or minus sqrt(2*2*2*7)=+ or - 2sqrt(14)

- myininaya

like when we did x^2=9
we got x=sqrt(9)=3 and x=-sqrt(9)=-3

- anonymous

okay. why not 2*sqrt7?

- myininaya

sqrt(8*7)=sqrt(2*2*2*7)=sqrt(4*14)=sqrt(4)sqrt(14)=2sqrt(14)

- myininaya

sqrt(ab)=sqrt(a)sqrt(b) is a rule you can use in the future k?

- anonymous

wow. you are very helpful. this is something i am lacking in my knowledge.... :)

- myininaya

thanks :)

- anonymous

give me a sec. i will attempt the original prob...

- anonymous

wow. i just did it! i can't believe i feel that i actually did it. haha :)
x^2=24
x=sqrt+-24
x=sqrt+-(6)sqrt+-(4)
x=+-2sqrt(6)
look like i'm understanding?

- myininaya

very nice but in the steps before don't put the +- inside the sqrt
x=+-sqrt(24)
x=+-sqrt(6)sqrt(4)
x=+-2sqrt(6)
but very nice otherwise :)
gj

- myininaya

can you do
x^2=54

- anonymous

i see. sorry. having internet issues here. :/

- anonymous

x=+or- 3sqrt(6)?

- anonymous

i believe this makes sense. :D i would like to know if the last one i did is correct :)

- anonymous

http://www.wolframalpha.com/input/?i=x^2%3D54
MHUAAHAHA!!! You are the best!

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