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some.random.cool.kid

  • one year ago

Solve the equation 4x2 + 8x + 1 = 0 by completing the square.

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  1. some.random.cool.kid
    • one year ago
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    @Hero @dan815 @iambatman

  2. some.random.cool.kid
    • one year ago
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    @phi @amistre64

  3. some.random.cool.kid
    • one year ago
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    @Nnesha mind helping :D

  4. some.random.cool.kid
    • one year ago
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    not to much this time...

  5. some.random.cool.kid
    • one year ago
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    @Nnesha

  6. anonymous
    • one year ago
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    First, make the coefficient of the x^2 term 1 by dividing both sides by 4.

  7. some.random.cool.kid
    • one year ago
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    ok

  8. some.random.cool.kid
    • one year ago
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    so 4 by which sides?

  9. anonymous
    • one year ago
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    Divide all terms on both sides of the equation by 4.

  10. some.random.cool.kid
    • one year ago
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    the x^2 and the 8x by 4?

  11. anonymous
    • one year ago
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    Everything, yes. What will it look like?

  12. some.random.cool.kid
    • one year ago
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    uh... well 8x would be 2x?

  13. anonymous
    • one year ago
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    Yup. Keep going.

  14. some.random.cool.kid
    • one year ago
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    and what about the ^2

  15. some.random.cool.kid
    • one year ago
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    is that 4^2?

  16. anonymous
    • one year ago
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    Divide 4x^2 by 4. What do you get?\[\frac{ 4x^2 }{ 4 } = ?\]

  17. some.random.cool.kid
    • one year ago
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    just x^2?

  18. anonymous
    • one year ago
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    Right. Keep going.

  19. some.random.cool.kid
    • one year ago
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    1 divided by 4 is that 4?

  20. anonymous
    • one year ago
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    No. It's \(\frac{1}{4}\). What about the right hand side? Gotta do that too.

  21. some.random.cool.kid
    • one year ago
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    0

  22. anonymous
    • one year ago
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    Good. So, dividing everything by 4 gives\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]OK so far?

  23. some.random.cool.kid
    • one year ago
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    alright

  24. anonymous
    • one year ago
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    Now, we don't want the 1/4 on the left hand side, so subtract 1/4 from both sides. What will it look like then?

  25. some.random.cool.kid
    • one year ago
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    uh - 1/4?

  26. some.random.cool.kid
    • one year ago
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    thats a negative

  27. anonymous
    • one year ago
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    OK. What does the whole equation look like now?

  28. some.random.cool.kid
    • one year ago
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    x^2 + 2x - 1/4?

  29. anonymous
    • one year ago
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    Not quite. What happened to the equals sign?

  30. some.random.cool.kid
    • one year ago
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    idk is it x^2 + 2x - 1/4 =0 or x^2 + 2x = 1/4?

  31. anonymous
    • one year ago
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    We better back up a step. You had\[x^2 + 2x + \frac{ 1 }{ 4 } = 0\]To get rid of the 1/4 on the left hand side, you need to subtract it. And the rules of equality say that whatever you do one side of the equation you have to do to the other side as well. So you have to subtract 1/4 from both sides. So\[x^2 + 2x + \frac{ 1 }{ 4 } - \frac{ 1 }{ 4 } = 0-\frac{ 1 }{ 4 }\]Simplify both sides. What will it look like?

  32. some.random.cool.kid
    • one year ago
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    wait but if you canceled the other 1/4ths and your left - 1/4 then what is left i dont get it all i se is x^2 + 2x - 1/4

  33. anonymous
    • one year ago
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    This is not an equation. What happened to the equal sign. It can't just disappear.

  34. some.random.cool.kid
    • one year ago
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    you dont have one you used it when you crossed out the 1/4ths

  35. some.random.cool.kid
    • one year ago
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    thats how i was tought...

  36. anonymous
    • one year ago
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    Sorry, no. Equals signs don't disappear. What you are left with is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]Do you understand?

  37. some.random.cool.kid
    • one year ago
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    ooo ok

  38. anonymous
    • one year ago
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    OK. So now you're ready to complete the square on the left hand side. Do you remember how to do it?

  39. some.random.cool.kid
    • one year ago
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    some more dividing? lawl

  40. anonymous
    • one year ago
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    Not really :) Do you know how to complete the square?

  41. some.random.cool.kid
    • one year ago
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    mm take half the sq on both sides?

  42. anonymous
    • one year ago
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    Something like that. You need to add a number to the left hand side that will make it a perfect square trinomial. Look at the coefficient of the 'x' term. Take half of that coefficient and then square it. What number do you get?

  43. some.random.cool.kid
    • one year ago
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    your left with x +2? after taking away one x from each of the sides?

  44. anonymous
    • one year ago
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    No. What is the coefficient of the 'x' term on the left hand side?

  45. some.random.cool.kid
    • one year ago
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    sorry idk that..

  46. anonymous
    • one year ago
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    What number is multiplying x on the left hand side?

  47. some.random.cool.kid
    • one year ago
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    1

  48. anonymous
    • one year ago
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    Oh my. The equation you're working with now is\[x^2 + 2x = -\frac{ 1 }{ 4 }\]The 'x' term on the left hand side is \(2x\). The coefficient is the number that is multiplying the \(x\). What number is it?

  49. some.random.cool.kid
    • one year ago
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    omg i said idk geez...

  50. anonymous
    • one year ago
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    |dw:1443484097406:dw|

  51. anonymous
    • one year ago
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    In \(2x\), the \(x\) is being multiplied by \(2\). The 2 is called the coefficient of x. Do you understand?

  52. some.random.cool.kid
    • one year ago
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    that is a variable you cant multiply that :/

  53. some.random.cool.kid
    • one year ago
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    you have to simplify it...

  54. anonymous
    • one year ago
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    Sure you can. 2 times x is 2x. 14 times y is 14y. And so on.

  55. some.random.cool.kid
    • one year ago
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    x equals start fraction three plus or minus square root of six end square root over two end fraction x equals six plus or minus two square root of six end square root x equals start fraction negative two plus or minus square root of three end square root over two end fraction x equals start fraction four plus or minus three square root of six end square root over eight end fraction

  56. anonymous
    • one year ago
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    So the coefficient of the 'x' term is 2. Now take half of the coefficient - half of 2 is 1. Now square that number. What is 1 squared?

  57. some.random.cool.kid
    • one year ago
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    1

  58. some.random.cool.kid
    • one year ago
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    anyways those are what i have...

  59. some.random.cool.kid
    • one year ago
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    im thinking its bewtween those...

  60. anonymous
    • one year ago
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    Very good. So you need to add 1 to both sides of the equation\[x^2 + 2x = -\frac{ 1 }{ 4 }\]What will the equation look like?

  61. some.random.cool.kid
    • one year ago
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    like this in the end... x equals start fraction four plus or minus three square root of six end square root over eight end fraction

  62. anonymous
    • one year ago
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    How do you get that?

  63. some.random.cool.kid
    • one year ago
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    out of these and based on your thing this was best choice. x equals start fraction three plus or minus square root of six end square root over two end fraction x equals six plus or minus two square root of six end square root x equals start fraction negative two plus or minus square root of three end square root over two end fraction x equals start fraction four plus or minus three square root of six end square root over eight end fraction

  64. anonymous
    • one year ago
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    If you would like my help in learning how to complete the square, I'll help you. But, if you're just going to copy someone else's work (which hasn't been reduced to lowest terms, by the way), then I'll move on. Good luck with your work.

  65. some.random.cool.kid
    • one year ago
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    this is my work lol

  66. some.random.cool.kid
    • one year ago
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    these were my answers and your answer werent near what i had...

  67. some.random.cool.kid
    • one year ago
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    @Nnesha

  68. anonymous
    • one year ago
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    You haven't completed the work required to arrive at an answer.

  69. some.random.cool.kid
    • one year ago
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    the way you were headed i figured i would paste my answers because it seemed like you were going in a different direction... as soon as you said i can multiply i knew it was off because in this course you do not multiply these it strictly says you dont multiply them its supposed to be simplified @ospreytriple

  70. some.random.cool.kid
    • one year ago
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    the variables i mean...

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