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anonymous

  • 2 years ago

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

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  1. SolomonZelman
    • 2 years ago
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    add 29 to both sides.

  2. SolomonZelman
    • 2 years ago
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    can you add 29 to both sides?

  3. anonymous
    • 2 years ago
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    which sides?

  4. SolomonZelman
    • 2 years ago
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    Both. \[x^2-12+7+29=0+29\]

  5. anonymous
    • 2 years ago
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    and why 29?

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

  7. Hero
    • 2 years ago
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    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. anonymous
    • 2 years ago
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    Oh. Okay. I still don't quite get it, but lets move on. What shall I do next? :D

  9. anonymous
    • 2 years ago
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    Uhh... which one is right?

  10. gorv
    • 2 years ago
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    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. anonymous
    • 2 years ago
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    Are all of these right, just in different ways?

  12. Hero
    • 2 years ago
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    You add 36 to both sides, not 29

  13. Hero
    • 2 years ago
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    But 36 - 7 = 29

  14. SolomonZelman
    • 2 years ago
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    @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. anonymous
    • 2 years ago
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    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
    • 2 years ago
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    @SolomanZelman, if that's true, then explain how I got my result

  17. gorv
    • 2 years ago
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    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
    • 2 years ago
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    I know exactly how the process works and what to add to both sides.

  19. SolomonZelman
    • 2 years ago
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    @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
    • 2 years ago
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    @hero if u will add 29 both side than on x^2-12x+7+29=29 x^2-12x+36=29

  21. Hero
    • 2 years ago
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    She'll only understand if those teaching know what they are talking about

  22. SolomonZelman
    • 2 years ago
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    STOP ARGUING!

  23. SolomonZelman
    • 2 years ago
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    YES, add 29

  24. gorv
    • 2 years ago
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    @hero plzz plzzzz plzzzz for god sake use little of ur mind

  25. SolomonZelman
    • 2 years ago
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    @Emily778, do you get how I came up with 29? Do you want to learn how to complete the square?

  26. Hero
    • 2 years ago
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    I think @Emily778 already has it figured out lol

  27. SolomonZelman
    • 2 years ago
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    MODERATOR, please don't ruin the thread, and confuse teh asker, lets teach her!

  28. anonymous
    • 2 years ago
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    @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
    • 2 years ago
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    Sorry If I was offensive, @Hero .

  30. Hero
    • 2 years ago
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    Finish solving for x @Emily778

  31. Hero
    • 2 years ago
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    Take the square root of both sides

  32. anonymous
    • 2 years ago
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    Can you show me how? I am so confused:(

  33. SolomonZelman
    • 2 years ago
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    @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
    • 2 years ago
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    to make the left side...typo

  35. Hero
    • 2 years ago
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    |dw:1384666594334:dw|

  36. SolomonZelman
    • 2 years ago
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    Emily, do you get it conceptually?

  37. Hero
    • 2 years ago
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    Add 6 to both sides to finish solving for x

  38. anonymous
    • 2 years ago
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    yep.

  39. anonymous
    • 2 years ago
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    so, like this @Hero (x-6)^2+6=29+6?

  40. Hero
    • 2 years ago
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    @Emily778, please observe what I did above first

  41. Hero
    • 2 years ago
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    I think you missed that last bit I posted in a drawing

  42. anonymous
    • 2 years ago
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    oh, you have to square root first?

  43. Hero
    • 2 years ago
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    Yes you can't do anything until you take the square root of both sides.

  44. Hero
    • 2 years ago
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    @SolomonZelman, I assure you that we're supposed to add 36 to both sides. I wouldn't tell you anything wrong here.

  45. Hero
    • 2 years ago
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    If you don't believe me, I have ways of convincing you.

  46. Hero
    • 2 years ago
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    For one, I know you would never argue with WolframAlpha.

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

  48. Hero
    • 2 years ago
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    Hang on, @SolomonZelman, WolframAlpha is undefeated.

  49. SolomonZelman
    • 2 years ago
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    I meant\[x^2-12x+7=0\]

  50. anonymous
    • 2 years ago
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    okay, so it's actually x-6+6=+=sqrt29=6?

  51. SolomonZelman
    • 2 years ago
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    Well yes it is then.

  52. nincompoop
    • 2 years ago
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    omg don't argue with @Hero

  53. SolomonZelman
    • 2 years ago
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    @Hero, I am sorry to say this, but you have to rvw over some staff.

  54. nincompoop
    • 2 years ago
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    he is correct and I am telling you it

  55. anonymous
    • 2 years ago
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    @hero okay, so it's actually x-6+6=+=sqrt29=6?

  56. nincompoop
    • 2 years ago
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    NOOOOOOOOOOOOOOO

  57. Hero
    • 2 years ago
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    http://tr.im/4klyc

  58. SolomonZelman
    • 2 years ago
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    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
    • 2 years ago
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    Don't tell me 1+1=4

  60. nincompoop
    • 2 years ago
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    I know I do not need a calculator and I know he is correct

  61. Hero
    • 2 years ago
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    Notice that wolframalpha says to add 36 to both sides.

  62. Hero
    • 2 years ago
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    In this here link: http://tr.im/4klyc

  63. SolomonZelman
    • 2 years ago
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    maybe you put in -7, instead of +7.

  64. SolomonZelman
    • 2 years ago
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    OK, when you subtract 7, but you can just add 29, without subtracting 7.

  65. SolomonZelman
    • 2 years ago
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    See?

  66. anonymous
    • 2 years ago
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    Thankyou! Is that it @Hero

  67. Hero
    • 2 years ago
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    There's only one correct way to do it @SolomonZelman. Wolframalpha shows the steps. Go review them.

  68. Hero
    • 2 years ago
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    @Emily778, I think you have it but review your symbology for mistakes and check the link on WolframAlpha

  69. SolomonZelman
    • 2 years ago
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    @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. anonymous
    • 2 years ago
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    okay

  71. SolomonZelman
    • 2 years ago
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    Do you guys just argue, or actually READ MY REPLIES?

  72. nincompoop
    • 2 years ago
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    solomon, study more before you question

  73. SolomonZelman
    • 2 years ago
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    @nincompoop, you obviously didn't understand what i said.

  74. nincompoop
    • 2 years ago
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    just study

  75. SolomonZelman
    • 2 years ago
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    Do you understand what I said, I don't need to study, I am fine.

  76. nincompoop
    • 2 years ago
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    study

  77. Hero
    • 2 years ago
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    @SolomonZelman, there's a difference between wasting steps and skipping steps.

  78. Hero
    • 2 years ago
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    Skipping steps leads to confusion

  79. SolomonZelman
    • 2 years ago
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    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
    • 2 years ago
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    I still think though, that emily didn't get it conceptually.

  81. nincompoop
    • 2 years ago
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    she never does...

  82. SolomonZelman
    • 2 years ago
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    That was quite offensive.

  83. Hero
    • 2 years ago
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    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
    • 2 years ago
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    True, and I was trying to ask emily if she figured out the first step(s) in completing the square.

  85. nincompoop
    • 2 years ago
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    doubt it

  86. SolomonZelman
    • 2 years ago
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    Yes, me too, that's why I kept on asking that.

  87. Hero
    • 2 years ago
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    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
    • 2 years ago
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    couldn't agree more

  89. SolomonZelman
    • 2 years ago
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    Well, not that they taught me that, but didn't get any points off.

  90. nincompoop
    • 2 years ago
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    it's cool can't teach someone about skipping when that person barely knows anything to begin with

  91. SolomonZelman
    • 2 years ago
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    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
    • 2 years ago
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    I see your point though....

  93. nincompoop
    • 2 years ago
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    1+1 = 4 though

  94. SolomonZelman
    • 2 years ago
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    And she still hasn't figure it out conceptually, just got the answer and left.

  95. SolomonZelman
    • 2 years ago
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    @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
    • 2 years ago
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    it's called precision

  97. SolomonZelman
    • 2 years ago
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    \(\huge {\color{green} {Yup,} }\) forgot the name for this, I learned that last year.

  98. nincompoop
    • 2 years ago
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    anyway, good night

  99. SolomonZelman
    • 2 years ago
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    you too!

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

  101. Hero
    • 2 years ago
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    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
    • 2 years ago
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    \[\(\huge {\color{green} {B^{Y^{E ^{!}}}} }\)\]

  103. SolomonZelman
    • 2 years ago
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    Didn't delete the parenthesis....

  104. Hero
    • 2 years ago
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    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
    • 2 years ago
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    This is a systematic approach and you end up with (x + b/2)^2 = b^2/4 + c

  106. SolomonZelman
    • 2 years ago
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    Well, then improper methodology just shows that the person who did the steps is SMART.

  107. Hero
    • 2 years ago
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    Now let's see @SolomonZelman explain his method in a systematic, generalized manner.

  108. SolomonZelman
    • 2 years ago
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    I would just use an example similar to the one we solved just now.

  109. Hero
    • 2 years ago
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    Examples are not generalized. And they don't show the systematic methodology.

  110. Hero
    • 2 years ago
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    Systematic methods have a better chance of being understood than non-systematic methods.

  111. SolomonZelman
    • 2 years ago
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    OK, I already said that I agree that to start teaching, systematic.... but not using it still shows that the solver is smarter.

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