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anonymous

  • one year ago

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

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  1. SolomonZelman
    • one year ago
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    first expand the product. (x+7)(x-9) = ?

  2. anonymous
    • one year ago
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    x^2-9x+7x-63

  3. SolomonZelman
    • one year ago
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    yes, (x + 7)(x – 9) = 25 x\(^2\)-9x+7x-63 = 25 add the x's on the left side, x\(^2\)-2x-63 = 25

  4. SolomonZelman
    • one year ago
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    Add 63 to both sides, and u then get?

  5. anonymous
    • one year ago
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    -38

  6. SolomonZelman
    • one year ago
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    x\(^2\)-2x-63 = 25 x\(^2\)-2x-63\(\small\color{red}{+63}\)= 25\(\small\color{red}{+63}\)

  7. SolomonZelman
    • one year ago
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    like that, add 63 to both sides. what do you get after doing this?

  8. anonymous
    • one year ago
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    ooooooooooh i see. x^2-2x= 88

  9. SolomonZelman
    • one year ago
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    yes, and then tell me what number would make the x²-2x +what a perfect square trinomial? (remember the rule DanJS posted: "half of the coefficient on x, then squared")

  10. anonymous
    • one year ago
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    1?

  11. SolomonZelman
    • one year ago
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    that number that makes the left hand side a perfect square trinomial, this number, you should add to both sides of the equation.

  12. SolomonZelman
    • one year ago
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    yes, it is 1.

  13. SolomonZelman
    • one year ago
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    So, add 1 to both sides

  14. SolomonZelman
    • one year ago
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    x\(^2\)-2x\(\small\color{blue}{+1}\)= 88\(\small\color{blue}{+1}\)

  15. SolomonZelman
    • one year ago
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    can you go on from here? steps just in case: \(1.\) simplify the right side \(2.\) factor the left side (it should look like " (x-number)² ") \(3.\) take the square root of both sides (and don't forget the \(\pm\)) \(4.\) add 1 to both sides of the equation

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