## Emily778 Group Title check for extraneous solutions. sqrt x+7-x=1 Please show step by step on how to do this. Thankyou. 10 months ago 10 months ago

1. RolyPoly

Let $$u=\sqrt{x}$$, then x = $$u^2$$ Now, the equation becomes $u+7-u^2=1$ Can you do it?

2. Emily778

Wat?

3. Emily778

@Krazete

4. Emily778

I don't get the way you're explaining it to me @RolyPoly

5. Krazete

Please make use of parentheses. The way you write problems is sorta confusing. Is it √(x+7)-x=1 or ...?

6. Emily778

I guess. Sorry, it doesn't show parentheses on my math problem.

7. RolyPoly

Is the equation (1)$$\sqrt{ x+7-x} =1$$ or (2) $$\sqrt{x}+7-x=1$$?

8. Emily778

nvm, i got the answer. Thx

9. Emily778

nvm.. I tried wolframalpha. But only get two step by steps each day:(

10. Emily778

I'll have to get the answer tomorrow.

11. RolyPoly

It would be better if you know how to solve it, instead of just relying on WolframAlpha.

12. Emily778

eh, true. But lets be honest with ourselves, I'm never going to use this advanced of math in the future.

13. Emily778

Honestly, I just need credits/passed classes

14. Emily778

you can argue all you want, but it's true.

15. RolyPoly

Don't want to argue, just want to help you pass the course and you can learn how to solve it at the same time :)

16. Emily778

can you just show me please? I'm 18 lessons behind:(

17. nikato

$\sqrt{x+7}-x=1$

18. nikato

19. Emily778

It would be a different story if I wasn't that behind

20. RolyPoly

$\sqrt{x-7-x}=1$$\sqrt{x-7}-x=1$$\sqrt{x}-7-x=1$ Which one is your question?

21. Emily778

like this @nikato |dw:1388896983931:dw|

22. Emily778

the 2nd one @RolyPoly

23. nikato

yup

24. Emily778

what next?

25. nikato

so now u have|dw:1388897108757:dw| now square both sides

26. Emily778

i know 9 is the solution

27. Emily778

what next?

28. nikato

did u square both sides. and simplified it?

29. Emily778

how do I simplify it?

30. nikato

|dw:1388897450469:dw|does that make sense?

31. Emily778

yeah.

32. Emily778

what next?

33. nikato

subtract x and 7 on both sides so that the equation equal 0

34. nikato

|dw:1388897691356:dw|

35. Emily778

what next? :D ha

36. nikato

|dw:1388897800670:dw| can u factor the right side?

37. Emily778

can you show me? eheh

38. nikato

|dw:1388898386363:dw|

39. Emily778

9?

40. Emily778

@nikato

41. Emily778

it has to be 9.

42. nikato

no, i dont think 9 is a solution. try pluggin it back into the origianl equation. it doesnt work

43. nikato

|dw:1388899069611:dw|

44. Emily778

then you did it wrong. Ugh. Wolfram said it was 9

45. nikato

no, im for sure 9 is not an answer. it doesnt make sense. its one fo those^

46. Emily778

@Krazete is he wrong or not?

47. Emily778

sorry, nikato. I gotta make sure.

48. nikato

yea, its fine. whatever u feel is right

49. Krazete

nikato's right.

50. Emily778

okayy,, it's just wolfram said the solution was 9. But I guess it's better to have something than nothing at all.

51. nikato

maybe u typed in the wrong equation in wolfrma

52. Krazete

Look at what Wolfram says under "input." Is it the same as your problem? It might've calculated √x instead of √(x+7). Parentheses are quite important.

53. Emily778

nikato, what do I do next? Sorry for doubting you

54. nikato

|dw:1388899779946:dw| solve for x. did most of the work. should be easy for u. there are suppose to be 2 answers

55. Emily778

one of them is 2.

56. nikato

yes. and the other?

57. Emily778

o?

58. nikato

no, -3. so now u want to find if there is anyextraneous answers

59. nikato

plug both back into the equation and see if they make sense|dw:1388900195738:dw|

60. Emily778

ugh. How much more is there??

61. Emily778

what next?

62. nikato

no, this is it. check if both of those equation are true. if they are not, then that "x" is extraneous

63. Emily778

it's 1.

64. Emily778

thanks. :p

65. nikato

WAIT NO. its either 2 or -3. i helped plug in both in for x the first one is x=2 and the other is x=-3

66. Emily778

67. nikato

no, thats not what i meant

68. nikato

|dw:1388901004098:dw|

69. Emily778

I'm sorry, I still don't get how you got those answers. I got -5 and 1. 1 was correct. -5 was incorrect.

70. nikato

yes. so that means -3 is the extraneous answer. remember how we worked the problem, and got 2 and -3 as the naswer. however when u plug -3 back into the original equation u get -5 instead of 1. which means the answer doesnt "work" which we call an extraneous answer

71. Emily778

72. nikato

just 2

73. nikato

becuz like i said ^ -3 is an extraneous solution

74. Emily778

so, I would put "x=2 only"?

75. nikato

yup