anonymous one year ago Arrg I need help AGAIN

1. anonymous

$x-8=-\sqrt{x ^{2}-8}$

2. anonymous

Solution or nah?

3. UsukiDoll

damn.. one sec.

4. 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

5. anonymous

ok I'm following you so far

6. UsukiDoll

$(x-8)(x-8)=-(x^2-8)$

7. UsukiDoll

expand the left = distribute the - on the right

8. UsukiDoll

can you do that? O_o

9. anonymous

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

10. UsukiDoll

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

11. UsukiDoll

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

12. UsukiDoll

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

13. UsukiDoll

in the name of Mathematics we shall expand LOL

14. anonymous

ohhhh yes i know what to do

15. UsukiDoll

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

16. anonymous

$x^2-16x+64=-x^2+8$ $-16x=-56$

17. UsukiDoll

ok then divide -16 on both sides

18. anonymous

x=3.5

19. anonymous

It seems like I did something wrong there though

20. UsukiDoll

oy keep it in fraction form

21. anonymous

$x=3\frac{ 1 }{ 2 }$

22. UsukiDoll

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

23. Michele_Laino

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

24. UsukiDoll

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

25. 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.

26. UsukiDoll

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

27. UsukiDoll

hello?

28. anonymous

I'm here just doing the math

29. anonymous

16x=72

30. Michele_Laino

yes! @UsukiDoll

31. UsukiDoll

ok so now divide 16 from both sides

32. anonymous

$x=\frac{ 9 }{ 2 }$

33. 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!

34. 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

35. UsukiDoll

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

36. anonymous

yeah thats where I'm at XD

37. UsukiDoll

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

38. anonymous

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

39. UsukiDoll

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

40. UsukiDoll

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

41. 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.

42. UsukiDoll

don't use decimals. It's a pain

43. UsukiDoll

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

44. UsukiDoll

$\frac{-7}{2} = -\sqrt{\frac{49}{4}}$

45. UsukiDoll

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

46. anonymous

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

47. UsukiDoll

yes

48. anonymous

cool thanks