## Emily778 2 years ago Solve the quadratic equation by completing the square. x^2-12x+7=0

1. SolomonZelman

2. SolomonZelman

can you add 29 to both sides?

3. Emily778

which sides?

4. SolomonZelman

Both. \[x^2-12+7+29=0+29\]

5. Emily778

and why 29?

6. SolomonZelman

To make the left side into perfect square because you have to have (-6) (-6) which equals 36.

7. Hero

x^2 - 12x + 7 = 0 x^2 - 12x = -7 x^2 - 12x + (-12/2)^2 = (-12/2)^2 - 7 x^2 - 12x + 36 = 36 - 7 (x - 6)^2 = 29 Take square root of both sides to finish solving for x

8. Emily778

Oh. Okay. I still don't quite get it, but lets move on. What shall I do next? :D

9. Emily778

Uhh... which one is right?

10. gorv

x^2-2*x*6+7=0 x^2-2*x*6+36-36+7=0 (x^2-2*x*6+36)-29=0 (x-6)^2-29=0 (x-6)^2=29 x-6=29^1/2 x=(29)^1/2+6

11. Emily778

Are all of these right, just in different ways?

12. Hero

You add 36 to both sides, not 29

13. Hero

But 36 - 7 = 29

14. SolomonZelman

@Hero, no you add 29, because that makes the left side into perfect square. @Emily778, I know what you are confused about, lets learn how to complete the square.

15. Emily778

I'll just do this x^2 - 12x + 7 = 0 x^2 - 12x = -7 x^2 - 12x + (-12/2)^2 = (-12/2)^2 - 7 x^2 - 12x + 36 = 36 - 7 (x - 6)^2 = 29

16. Hero

@SolomanZelman, if that's true, then explain how I got my result

17. gorv

actually in (a+b)^2=a^2+b^2+2ab here 2ab is 12x=2*x*6 so u need to make b^2 that is 36

18. Hero

I know exactly how the process works and what to add to both sides.

19. SolomonZelman

@Emily778, do you get how I came up with 29? lets do a different example. GUYS PLEASE, LETS TEACH HER, NOT DO HER WORK> She needs to understand.

20. gorv

@hero if u will add 29 both side than on x^2-12x+7+29=29 x^2-12x+36=29

21. Hero

She'll only understand if those teaching know what they are talking about

22. SolomonZelman

STOP ARGUING!

23. SolomonZelman

24. gorv

@hero plzz plzzzz plzzzz for god sake use little of ur mind

25. SolomonZelman

@Emily778, do you get how I came up with 29? Do you want to learn how to complete the square?

26. Hero

I think @Emily778 already has it figured out lol

27. SolomonZelman

28. Emily778

@Hero What do I do after this? Or is it already done? x^2 - 12x + 7 = 0 x^2 - 12x = -7 x^2 - 12x + (-12/2)^2 = (-12/2)^2 - 7 x^2 - 12x + 36 = 36 - 7 (x - 6)^2 = 29

29. SolomonZelman

Sorry If I was offensive, @Hero .

30. Hero

Finish solving for x @Emily778

31. Hero

Take the square root of both sides

32. Emily778

Can you show me how? I am so confused:(

33. SolomonZelman

@Emily778 PLEASE read this CAREFULLY. Do you know how to come up with the number that you have to add to both sides to ake the left side into a perfect square?

34. SolomonZelman

to make the left side...typo

35. Hero

|dw:1384666594334:dw|

36. SolomonZelman

Emily, do you get it conceptually?

37. Hero

Add 6 to both sides to finish solving for x

38. Emily778

yep.

39. Emily778

so, like this @Hero (x-6)^2+6=29+6?

40. Hero

@Emily778, please observe what I did above first

41. Hero

I think you missed that last bit I posted in a drawing

42. Emily778

oh, you have to square root first?

43. Hero

Yes you can't do anything until you take the square root of both sides.

44. Hero

@SolomonZelman, I assure you that we're supposed to add 36 to both sides. I wouldn't tell you anything wrong here.

45. Hero

If you don't believe me, I have ways of convincing you.

46. Hero

For one, I know you would never argue with WolframAlpha.

47. SolomonZelman

Hero, how does 36 make the left side into a perfect square, it is \[x^2+12x+7=0\]

48. Hero

Hang on, @SolomonZelman, WolframAlpha is undefeated.

49. SolomonZelman

I meant\[x^2-12x+7=0\]

50. Emily778

okay, so it's actually x-6+6=+=sqrt29=6?

51. SolomonZelman

Well yes it is then.

52. nincompoop

omg don't argue with @Hero

53. SolomonZelman

@Hero, I am sorry to say this, but you have to rvw over some staff.

54. nincompoop

he is correct and I am telling you it

55. Emily778

@hero okay, so it's actually x-6+6=+=sqrt29=6?

56. nincompoop

NOOOOOOOOOOOOOOO

57. Hero
58. SolomonZelman

Do you guys know how to complete the square, you don't need any online calculator for this. Idk how to even tell you this. you help with hard staff that I have no clue about, and make a simple error, in completing a square.

59. SolomonZelman

Don't tell me 1+1=4

60. nincompoop

I know I do not need a calculator and I know he is correct

61. Hero

Notice that wolframalpha says to add 36 to both sides.

62. Hero

63. SolomonZelman

maybe you put in -7, instead of +7.

64. SolomonZelman

OK, when you subtract 7, but you can just add 29, without subtracting 7.

65. SolomonZelman

See?

66. Emily778

Thankyou! Is that it @Hero

67. Hero

There's only one correct way to do it @SolomonZelman. Wolframalpha shows the steps. Go review them.

68. Hero

@Emily778, I think you have it but review your symbology for mistakes and check the link on WolframAlpha

69. SolomonZelman

@Hero it wastes a step on subtracting 7 from both sides, you still get the same thing, \[x^2-12+36=29\] Do you see my point?

70. Emily778

okay

71. SolomonZelman

Do you guys just argue, or actually READ MY REPLIES?

72. nincompoop

solomon, study more before you question

73. SolomonZelman

@nincompoop, you obviously didn't understand what i said.

74. nincompoop

just study

75. SolomonZelman

Do you understand what I said, I don't need to study, I am fine.

76. nincompoop

study

77. Hero

@SolomonZelman, there's a difference between wasting steps and skipping steps.

78. Hero

79. SolomonZelman

I am not saying the Wolframalpha is wrong, it just has a different way of showing... Yes, my bad, perhaps I skipped it, not wasted.... My teacher told me that both ways are valid, and to me that makes perfect sense. And YES, instead of arguing lets continue studying.

80. SolomonZelman

I still think though, that emily didn't get it conceptually.

81. nincompoop

she never does...

82. SolomonZelman

That was quite offensive.

83. Hero

Yes, but some things can be figured out through self-study, observation and understanding. One thing is for sure. She surely won't get it if she is fed incorrect info.

84. SolomonZelman

True, and I was trying to ask emily if she figured out the first step(s) in completing the square.

85. nincompoop

doubt it

86. SolomonZelman

Yes, me too, that's why I kept on asking that.

87. Hero

By the way @SolomonZelman, I'm fully aware of your method of doing it. But I abandoned it after I realized that steps were being skipped. It is wrong for teachers to teach it that way.

88. nincompoop

couldn't agree more

89. SolomonZelman

Well, not that they taught me that, but didn't get any points off.

90. nincompoop

it's cool can't teach someone about skipping when that person barely knows anything to begin with

91. SolomonZelman

I don't really see the difference between subtracting seven at first or not. To me it makes perfect sense to do my way.

92. SolomonZelman

93. nincompoop

1+1 = 4 though

94. SolomonZelman

And she still hasn't figure it out conceptually, just got the answer and left.

95. SolomonZelman

@nincompoop, actually in biology that could be true, like when parents (or future parents) combine or whatever the word for that is... LIKE twins.

96. nincompoop

it's called precision

97. SolomonZelman

\(\huge {\color{green} {Yup,} }\) forgot the name for this, I learned that last year.

98. nincompoop

anyway, good night

99. SolomonZelman

you too!

100. SolomonZelman

\(\huge {\color{green} {H} }\)\(\huge {\color{blue} {a} }\)\(\huge {\color{red} {v} }\)\(\huge {\color{orange} {e} }\) \(\huge {\color{purple} {a} }\) \(\huge {\color{lightblue} {n} }\)\(\huge {\color{grey} {i} }\)\(\huge {\color{brown} {g} }\)\(\huge {\color{lightgreen} {h} }\)\(\huge {\color{yellow }{t} }\)\(\huge {\color{darkgreen } {!} }\)

101. Hero

The difference between the methods is, one is systematic, and the other is not. The non-systematic method is an approach that some would refer to as improper methodology.

102. SolomonZelman

\[\(\huge {\color{green} {B^{Y^{E ^{!}}}} }\)\]

103. SolomonZelman

Didn't delete the parenthesis....

104. Hero

The method I use can be generalized to this: You begin with x^2 + bx - c = 0 add c to both sides: x^2 + bx = c Then add (b/2)^2 to both sides: x^2 + bx + (b/2)^2 = (b/2)^2 + c

105. Hero

This is a systematic approach and you end up with (x + b/2)^2 = b^2/4 + c

106. SolomonZelman

Well, then improper methodology just shows that the person who did the steps is SMART.

107. Hero

Now let's see @SolomonZelman explain his method in a systematic, generalized manner.

108. SolomonZelman

I would just use an example similar to the one we solved just now.

109. Hero

Examples are not generalized. And they don't show the systematic methodology.

110. Hero

Systematic methods have a better chance of being understood than non-systematic methods.

111. SolomonZelman

OK, I already said that I agree that to start teaching, systematic.... but not using it still shows that the solver is smarter.