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some.random.cool.kid

  • one year ago

Solve the quadratic equation x2 − 6x + 13 = 0 using the quadratic formula. What is the solution when expressed in the form a ± bi, where a and b are real numbers? x = 3 ± 2i x = 2 ± 3i x = 3 ± 4i x equals start fraction three plus or minus two i over two end fraction

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  1. some.random.cool.kid
    • one year ago
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    please walk me thorugh...

  2. some.random.cool.kid
    • one year ago
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    through* to get the right answr. @Nnesha

  3. some.random.cool.kid
    • one year ago
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    @peachpi

  4. some.random.cool.kid
    • one year ago
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    @pooja195

  5. some.random.cool.kid
    • one year ago
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    @DanJS @Data_LG2 @dan815 @triciaal

  6. DanJS
    • one year ago
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    you know the quadratic formula that results from solving that standrard quadratic form for x =

  7. some.random.cool.kid
    • one year ago
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    i knew it but forgot mind showing me it?

  8. DanJS
    • one year ago
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    If ax^2 + bx + c = 0 \[x = \frac{ -b \pm \sqrt{b^2-4ac} }{ 2a}\]

  9. some.random.cool.kid
    • one year ago
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    yes yess ik that ah thank ok so b is b 13 is c and 1 is a correct?

  10. some.random.cool.kid
    • one year ago
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    thank you*

  11. some.random.cool.kid
    • one year ago
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    oops i said b is bxD

  12. some.random.cool.kid
    • one year ago
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    i meant b is 6

  13. DanJS
    • one year ago
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    a = 1 b = -6 c = 13

  14. some.random.cool.kid
    • one year ago
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    oops -6 not 6 ok

  15. DanJS
    • one year ago
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    x^2 + (-6)x .....

  16. some.random.cool.kid
    • one year ago
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    uh solve that?

  17. some.random.cool.kid
    • one year ago
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    want me to solve it?

  18. DanJS
    • one year ago
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    yeah , use those values and simplify as much as you can

  19. some.random.cool.kid
    • one year ago
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    uh...wait step by step please what will this look like when finished finding each letter ot the number? can you rewrite for me but this time instead of variables substitute it with numbers so that i may have an idea in my mind i do better solving when i have a visual.

  20. DanJS
    • one year ago
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    ill type it out fast, i have to run for a while ... one sec

  21. some.random.cool.kid
    • one year ago
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    ok thank you

  22. DanJS
    • one year ago
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    the battery died in my mouse right after that comment, sorry took forever to find a new one

  23. DanJS
    • one year ago
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    \[x = \frac{ - (-6) \pm \sqrt{(-6)^2-4*1*13} }{ 2*1 }\]

  24. DanJS
    • one year ago
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    \[x = \frac{ 6 \pm \sqrt{-16} }{ 2 }\]

  25. DanJS
    • one year ago
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    the square root of a negative is not in the real numbers, for the complex, remember that the imaginary number i = square root of -1

  26. some.random.cool.kid
    • one year ago
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    so so do i find the sqrt now because its 4

  27. DanJS
    • one year ago
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    \[x = \frac{ 6 \pm \sqrt{16 * -1} }{ 2 } = \frac{ 6 \pm \sqrt{16}*\sqrt{-1} }{ 2 }\]

  28. DanJS
    • one year ago
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    replace root of -1 with that imaginary I symbol , then just have to simplify by dividing 2 into the top , root 16 is 4

  29. some.random.cool.kid
    • one year ago
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    i did say 4 its above

  30. DanJS
    • one year ago
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    \[x = \frac{ 6 \pm 4*i}{ 2 } = 3 \pm 2i\]

  31. some.random.cool.kid
    • one year ago
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    isnt that the simpliest of forms?

  32. some.random.cool.kid
    • one year ago
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    so quick question do you have time for two more?

  33. DanJS
    • one year ago
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    yeah, that is a conjugate pair, complex numbers come in pairs like that ..+ and -

  34. DanJS
    • one year ago
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    x = 3 + 2i and x = 3 - 2i

  35. some.random.cool.kid
    • one year ago
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    you've been the only great help today that was able to explain in manor that i understood hope you have more time for jus two more.

  36. DanJS
    • one year ago
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    sure , i can spend like 10 min prolly

  37. some.random.cool.kid
    • one year ago
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    great that should be enough. next one says -

  38. some.random.cool.kid
    • one year ago
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    Solve the equation 4x2 + 8x + 1 = 0 by completing the square. 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

  39. some.random.cool.kid
    • one year ago
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    is this same method or is this the other method with teh factoring?

  40. DanJS
    • one year ago
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    completing square, you want to turn the ax^2 + bx + c into something that will factor into (term)*(term) or (term)^2, which are sides of equal length of a square..

  41. DanJS
    • one year ago
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    as now you cant... 4x^2 + 8x + 1 = 0

  42. DanJS
    • one year ago
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    you can add something to both sides of the equations so that you find a value that will factor 4x^2 + 8x + c The thing to remember is that you just take half of b^2

  43. DanJS
    • one year ago
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    (b=8) [ b/2]^2 = [8/2]^2 = 16

  44. some.random.cool.kid
    • one year ago
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    so 8/2^2?

  45. some.random.cool.kid
    • one year ago
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    oh yeah

  46. DanJS
    • one year ago
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    add 16 to both sides of the quadratic like this... (4x^2 + 8x + 16) + 1 = 0 + 16

  47. DanJS
    • one year ago
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    factorable now, and simplify

  48. DanJS
    • one year ago
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    4(x^2 + 2x + 4) = 16 - 1

  49. some.random.cool.kid
    • one year ago
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    mmm wait you had me and then lost me lol so what am i factoring the 16 8x and the other one if so how do i go about doing this, by finding the common multiple?

  50. DanJS
    • one year ago
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    The reason to add (b/2)^2 = 16 to both sides, was because that will make the first two terms in the quadratic a perfect square with it... factors easy

  51. DanJS
    • one year ago
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    see i added the 16 and grouped it with the 4x^2 + 8x + 16 ready to factor

  52. some.random.cool.kid
    • one year ago
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    alright so...

  53. DanJS
    • one year ago
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    4(x^2 + 2x + 4) = 16 - 1

  54. DanJS
    • one year ago
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    x^2 + 2x + 4 = 15/4 (x + 2)*(x + 2) = 15/4

  55. some.random.cool.kid
    • one year ago
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    15/4 = 3.75 correct?

  56. some.random.cool.kid
    • one year ago
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    still there?

  57. some.random.cool.kid
    • one year ago
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    mouse died again? lawl

  58. DanJS
    • one year ago
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    no , messed up, answer was wrong... i see where now... before you complete the square by adding on that half b squared term, you have to simplify the 4x^2 + 8x terms first by taking the factor of 4 out...

  59. DanJS
    • one year ago
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    i will type it all

  60. DanJS
    • one year ago
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    4x^2 + 8x + 1 = 0 4*(x^2 + 2x) + 1 = 0 x^2 + 2x = -1/4 now complete square

  61. DanJS
    • one year ago
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    x^2 + 2x + 1 = -1/4 + 1 (x + 1)^2 = 3/4

  62. some.random.cool.kid
    • one year ago
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    mmm ok

  63. some.random.cool.kid
    • one year ago
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    is there something i should do next?

  64. some.random.cool.kid
    • one year ago
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    dont leave ill be right back using the restroom real quick.

  65. DanJS
    • one year ago
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    yeah take the square root of both sides, which recall has a + and a - value then subtract the 1 to isolate x

  66. DanJS
    • one year ago
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    \[x+1 =\pm \sqrt{3/2} = \frac{ \pm \sqrt{3} }{ 2 }\] \[x = \frac{ \pm \sqrt{3} }{ 2 } - 1\]

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

  68. some.random.cool.kid
    • one year ago
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    whats next?

  69. DanJS
    • one year ago
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    that is the answer, i was looking at the choices... x equals start fraction negative two plus or minus square root of three end square root over two end fraction

  70. some.random.cool.kid
    • one year ago
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    this should end with -2 + or minus sqrt of 3 all over two correct?

  71. some.random.cool.kid
    • one year ago
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    oh nvm you just said that...

  72. DanJS
    • one year ago
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    they wrote it as a single fraction, one last step i guess if you wanted.... replace the -1 with - 2/2

  73. DanJS
    • one year ago
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    then combine into a single fraction

  74. some.random.cool.kid
    • one year ago
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    k got it :D this prob took longer than i thought sure you still have time for the last one?

  75. DanJS
    • one year ago
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    cuz i f'ed up in like the first step.. hah

  76. some.random.cool.kid
    • one year ago
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    lol

  77. DanJS
    • one year ago
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    remember to put the thing into simler form next time before anything else

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

  79. DanJS
    • one year ago
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    simplest form, standard form

  80. DanJS
    • one year ago
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    sure , quickly,

  81. some.random.cool.kid
    • one year ago
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    k great

  82. some.random.cool.kid
    • one year ago
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    What are the zeros for the function f(x) = 3x2 + 2x + 2 and how many times does the graph cross the x-axis? x equals start fraction negative one plus or minus i square root of seven end square root over three end fraction comma one time x equals start fraction negative one plus or minus i square root of five end square root over three end fraction comma never x equals start fraction negative two plus or minus two i square root of five end square root over three end fraction comma two times x equals start fraction negative one plus or minus five i over three end fraction comma never

  83. some.random.cool.kid
    • one year ago
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    i believe i got this one i thnk its d but it could also be the other never..

  84. some.random.cool.kid
    • one year ago
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    my teach said it would be never but idk which one i figured the imaginary number but i might be wrong.

  85. DanJS
    • one year ago
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    zeroes are x-intercept values, y = f(x) = 0 0 = 3x^2+2x+2

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

  87. DanJS
    • one year ago
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    it is the second one , x equals start fraction negative one plus or minus i square root of five end square root over three end fraction comma never

  88. some.random.cool.kid
    • one year ago
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    man so it was the second one darn knew it could figure out which one thanks i almost would have said the one because after i solved it i gave up on trying to figure out whether it was an imag or no...

  89. DanJS
    • one year ago
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    that one you just hav eto put the numumbers into tha tquadratic formula for a = 3 b=2 c=2

  90. some.random.cool.kid
    • one year ago
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    thank you for your help and patience. night i am done with this review my next i dont think requires assistant so i will let you go now :~>

  91. DanJS
    • one year ago
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    yeah no real zeros, just complex roots

  92. DanJS
    • one year ago
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    complex zeros

  93. DanJS
    • one year ago
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    k, i should be on here tomorrow , not sure

  94. some.random.cool.kid
    • one year ago
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    :D i pasted all this as review for my EOC at the end of this semester well midterm ...

  95. some.random.cool.kid
    • one year ago
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    ok thats perfect

  96. some.random.cool.kid
    • one year ago
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    do you have an idea of what time tomorrow i have some more stuff thats related to this...

  97. some.random.cool.kid
    • one year ago
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    i can hopefully use these as notes...

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