Arrg I need help AGAIN

- anonymous

Arrg I need help AGAIN

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- anonymous

\[x-8=-\sqrt{x ^{2}-8}\]

- anonymous

Solution or nah?

- UsukiDoll

damn.. one sec.

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## More answers

- UsukiDoll

there is a solution... but I'm trying to figure it out... unless we square both sides..
but that - has to be outside so it needs to be something like\[(x-8)^2=-(\sqrt{x ^{2}-8})^2\] then on the right hand side distribute the negative
for the left hand side expand

- anonymous

ok I'm following you so far

- UsukiDoll

\[(x-8)(x-8)=-(x^2-8) \]

- UsukiDoll

expand the left = distribute the - on the right

- UsukiDoll

can you do that? O_o

- anonymous

uhh I'm not sure what it means but i think i could if i know what it was lol

- UsukiDoll

use foil for the left hand side of the equation = distribute the negative sign

- UsukiDoll

\[(x-8)(x-8)=-(x^2-8) \]
I'll do the easy part then you can do the hard one ^_^
\[(x-8)(x-8)=-x^2+8 \]

- UsukiDoll

use FOIL method for (x-8)(x-8)

- UsukiDoll

in the name of Mathematics we shall expand LOL

- anonymous

ohhhh yes i know what to do

- UsukiDoll

once that is done.. get the variables to the left and put all numbers to the right

- anonymous

\[x^2-16x+64=-x^2+8\] \[-16x=-56\]

- UsukiDoll

ok then divide -16 on both sides

- anonymous

x=3.5

- anonymous

It seems like I did something wrong there though

- UsukiDoll

oy keep it in fraction form

- anonymous

\[x=3\frac{ 1 }{ 2 }\]

- UsukiDoll

something is off. the denominator part is right.. but not the numerator... it's supposed to be x= 9/2

- Michele_Laino

hint:
we can rewrite the original equation as below:
\[\Large \sqrt {{x^2} - 8} = 8 - x\]

- UsukiDoll

ok but that would be that we need to square both sides right?

- UsukiDoll

\[x^2-8=(8-x)(8-x) \]
\[x^2-8=64-8x-8x+x^2\]
\[x^2-8=64-16x+x^2\]
oh I think I see how it will work now.

- UsukiDoll

now try bringing all variables to the left and all numbers to the right

- UsukiDoll

hello?

- anonymous

I'm here just doing the math

- anonymous

16x=72

- Michele_Laino

yes! @UsukiDoll

- UsukiDoll

ok so now divide 16 from both sides

- anonymous

\[x=\frac{ 9 }{ 2 }\]

- UsukiDoll

I was trying to get a step by step solution to see how the 9 happen but these sites... I swear they love making a profit off of people for the whole guide.
yes! WE GOT IT!

- UsukiDoll

whoops ._>
I think we should've have
\[(x-8)^2=(-\sqrt{x ^{2}-8})^2\]
\[(x-8)(x-8)=x^2-8\]
\[x^2-16x+64=x^2-8\]
allaaalalal and it should be x =9/2

- UsukiDoll

-16x=-72
x = 9/2 x.x

- anonymous

yeah thats where I'm at XD

- UsukiDoll

it's been a while.. now I just refreshed my memory... include all signs when squaring both sides XD

- anonymous

lol so I'm having a bit of trouble checking it because its a fraction >.< I hate fractions

- UsukiDoll

\[\frac{9}{2}-8=-\sqrt{(\frac{9}{2}) ^{2}-8}\]

- UsukiDoll

\[\frac{9}{2}-8=-\sqrt{(\frac{81}{4}) -8}\] then use lcd

- anonymous

Ok so I used a decimal instead and i got 9.25=8.25 so I think there is no solution but I'm not sure if I did the math right.

- UsukiDoll

don't use decimals. It's a pain

- UsukiDoll

\[\frac{9}{2}-\frac{16}{2}=-\sqrt{(\frac{81}{4}) -\frac{32}{4}}\]

- UsukiDoll

\[\frac{-7}{2} = -\sqrt{\frac{49}{4}} \]

- UsukiDoll

take the square root of 49 and 4.. it's magic :)

- anonymous

Oh ok so -7/2=-7/2

- UsukiDoll

yes

- anonymous

cool thanks

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