Arrg I need help AGAIN

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Arrg I need help AGAIN

Mathematics
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\[x-8=-\sqrt{x ^{2}-8}\]
Solution or nah?
damn.. one sec.

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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
ok I'm following you so far
\[(x-8)(x-8)=-(x^2-8) \]
expand the left = distribute the - on the right
can you do that? O_o
uhh I'm not sure what it means but i think i could if i know what it was lol
use foil for the left hand side of the equation = distribute the negative sign
\[(x-8)(x-8)=-(x^2-8) \] I'll do the easy part then you can do the hard one ^_^ \[(x-8)(x-8)=-x^2+8 \]
use FOIL method for (x-8)(x-8)
in the name of Mathematics we shall expand LOL
ohhhh yes i know what to do
once that is done.. get the variables to the left and put all numbers to the right
\[x^2-16x+64=-x^2+8\] \[-16x=-56\]
ok then divide -16 on both sides
x=3.5
It seems like I did something wrong there though
oy keep it in fraction form
\[x=3\frac{ 1 }{ 2 }\]
something is off. the denominator part is right.. but not the numerator... it's supposed to be x= 9/2
hint: we can rewrite the original equation as below: \[\Large \sqrt {{x^2} - 8} = 8 - x\]
ok but that would be that we need to square both sides right?
\[x^2-8=(8-x)(8-x) \] \[x^2-8=64-8x-8x+x^2\] \[x^2-8=64-16x+x^2\] oh I think I see how it will work now.
now try bringing all variables to the left and all numbers to the right
hello?
I'm here just doing the math
16x=72
ok so now divide 16 from both sides
\[x=\frac{ 9 }{ 2 }\]
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!
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
-16x=-72 x = 9/2 x.x
yeah thats where I'm at XD
it's been a while.. now I just refreshed my memory... include all signs when squaring both sides XD
lol so I'm having a bit of trouble checking it because its a fraction >.< I hate fractions
\[\frac{9}{2}-8=-\sqrt{(\frac{9}{2}) ^{2}-8}\]
\[\frac{9}{2}-8=-\sqrt{(\frac{81}{4}) -8}\] then use lcd
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.
don't use decimals. It's a pain
\[\frac{9}{2}-\frac{16}{2}=-\sqrt{(\frac{81}{4}) -\frac{32}{4}}\]
\[\frac{-7}{2} = -\sqrt{\frac{49}{4}} \]
take the square root of 49 and 4.. it's magic :)
Oh ok so -7/2=-7/2
yes
cool thanks

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