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Janu16

  • one year ago

Which of the following values "completes the square," or creates a perfect square trinomial, for x2 + 10x + ___?

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  1. Janu16
    • one year ago
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    @SolomonZelman

  2. SolomonZelman
    • one year ago
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    Ok

  3. Janu16
    • one year ago
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    so how do you figure out the third number

  4. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) do you understand this rule?

  5. Janu16
    • one year ago
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    yaa but is there a name for this stuff

  6. Janu16
    • one year ago
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    i actually take online class and they haven't teached the rules you are teaching me

  7. SolomonZelman
    • one year ago
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    Oh, then you are a little bit behind, I guess.

  8. SolomonZelman
    • one year ago
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    I don't recall its name in particular, but I don't think that matters that much,.

  9. Janu16
    • one year ago
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    they have teached me y=a(x-h)^2+h and ax^2+bx+c for this lessom

  10. Janu16
    • one year ago
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    y=a(x-h)^2+k

  11. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2= }\) \(\large\color{black}{ \displaystyle (x+\color{red}{ a})(x+\color{red}{ a})= }\) \(\large\color{black}{ \displaystyle x\cdot x+x\cdot\color{red}{ a}+x\cdot \color{red}{ a}+\color{red}{ a}\cdot\color{red}{ a}= }\) \(\large\color{black}{ \displaystyle x^2+x\color{red}{ a}+x \color{red}{ a}+\color{red}{ a}^2= }\) \(\large\color{black}{ \displaystyle x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) `--------------------------------------------` Is this process I did familiar to you?

  12. Janu16
    • one year ago
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    yaas

  13. Janu16
    • one year ago
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    this is what i learned

  14. SolomonZelman
    • one year ago
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    ok, so thus we know that: \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) Okay?

  15. Janu16
    • one year ago
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    mhm

  16. SolomonZelman
    • one year ago
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    and we want to get \(x^2+10x\) peace of the equation, to be a perfect square.

  17. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle x^2+10x+{?} }\)

  18. SolomonZelman
    • one year ago
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    (you want to get your equation to be like: \(\large\color{black}{ \displaystyle (x+\color{red}{ a})^2=x^2+2\color{red}{ a}x+\color{red}{ a}^2 }\) )

  19. SolomonZelman
    • one year ago
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    10 is same as 2a, right?

  20. Janu16
    • one year ago
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    ook

  21. SolomonZelman
    • one year ago
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    Compere these two: \(\large\color{black}{ \displaystyle x^2+10x+{?} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)

  22. SolomonZelman
    • one year ago
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    Compare*

  23. SolomonZelman
    • one year ago
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    ((the question mark is \(a^2\) ))

  24. SolomonZelman
    • one year ago
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    so if 10 is 2a, then \(a^2\) is going to be equal to what?

  25. Janu16
    • one year ago
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    soory hold on im lagging

  26. Janu16
    • one year ago
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    2ax? or a2

  27. SolomonZelman
    • one year ago
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    Again, 2a in our case is what?

  28. Janu16
    • one year ago
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    10

  29. SolomonZelman
    • one year ago
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    so if 2a=10 then a\(^2\)=?

  30. Janu16
    • one year ago
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    10?

  31. SolomonZelman
    • one year ago
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    ok, 2a=10 then a=?

  32. Janu16
    • one year ago
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    im really not sure about thiss

  33. SolomonZelman
    • one year ago
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    2a=10 divide by 2 on both sides, and you get that a=5

  34. Janu16
    • one year ago
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    wait oyu divide?

  35. SolomonZelman
    • one year ago
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    Yes, if 2 times a is 10. Then one a is 5.

  36. Janu16
    • one year ago
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    ohhok so divide so the last blank would be 5

  37. SolomonZelman
    • one year ago
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    (( a\(^2\) is same as \(a \times a\). )) So, if a is 5, then \(a \times a\) is \(5\times 5\). That will be equal to \(25\).

  38. Janu16
    • one year ago
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    5^2? right

  39. SolomonZelman
    • one year ago
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    yes, and that is same thing as "5×5". And this is going to be equal to 25 as you know.

  40. SolomonZelman
    • one year ago
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    So, now you have: \(\large\color{black}{ \displaystyle x^2+10x+{\underline{25}} }\) \(\large\color{blue}{ \displaystyle x^2+2ax+a^2 }\)

  41. Janu16
    • one year ago
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    ohok and what was tht formula you used? I just wanna write it down

  42. SolomonZelman
    • one year ago
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    \(\LARGE\color{black}{ \displaystyle \color{blue}{x}^2+2\color{red}{a}\color{blue}{x}+\color{red}{a}^2=(\color{blue}{x}+\color{red}{a})^2 }\)

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