## anonymous 2 years ago check for extraneous solutions. sqrt x+7-x=1 Please show step by step on how to do this. Thankyou.

1. anonymous

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

2. anonymous

Wat?

3. anonymous

@Krazete

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. anonymous

nvm, i got the answer. Thx

9. anonymous

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

10. anonymous

I'll have to get the answer tomorrow.

11. anonymous

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

12. anonymous

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

13. anonymous

Honestly, I just need credits/passed classes

14. anonymous

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

15. anonymous

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. anonymous

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

17. nikato

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

18. nikato

19. anonymous

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

20. anonymous

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

21. anonymous

like this @nikato |dw:1388896983931:dw|

22. anonymous

the 2nd one @RolyPoly

23. nikato

yup

24. anonymous

what next?

25. nikato

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

26. anonymous

i know 9 is the solution

27. anonymous

what next?

28. nikato

did u square both sides. and simplified it?

29. anonymous

how do I simplify it?

30. nikato

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

31. anonymous

yeah.

32. anonymous

what next?

33. nikato

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

34. nikato

|dw:1388897691356:dw|

35. anonymous

what next? :D ha

36. nikato

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

37. anonymous

can you show me? eheh

38. nikato

|dw:1388898386363:dw|

39. anonymous

9?

40. anonymous

@nikato

41. anonymous

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. anonymous

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. anonymous

@Krazete is he wrong or not?

47. anonymous

sorry, nikato. I gotta make sure.

48. nikato

yea, its fine. whatever u feel is right

49. anonymous

nikato's right.

50. anonymous

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. anonymous

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. anonymous

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. anonymous

one of them is 2.

56. nikato

yes. and the other?

57. anonymous

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. anonymous

ugh. How much more is there??

61. anonymous

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. anonymous

it's 1.

64. anonymous

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. anonymous

67. nikato

no, thats not what i meant

68. nikato

|dw:1388901004098:dw|

69. anonymous

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. anonymous

72. nikato

just 2

73. nikato

becuz like i said ^ -3 is an extraneous solution

74. anonymous

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

75. nikato

yup