anonymous
  • anonymous
Arrg I need help AGAIN
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
\[x-8=-\sqrt{x ^{2}-8}\]
anonymous
  • anonymous
Solution or nah?
UsukiDoll
  • UsukiDoll
damn.. one sec.

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

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