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Math Help - Is this a textbook error or...

  1. #1
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    Is this a textbook error or...

    I'm currently going through some questions in my textbook and came across a question on a quadratic and linear simultaneous equation.

    Solve the equation:
    x + y = 1
    x^2 + y^2 = 16

    I am not interested in the question itself but rather the explanation the book gives me which says after a couple of steps shows the equation:

    2x^2 - 2x -15 = 0

    Then it tells me to divide the equation by 2 and says when you divide the equation by 2 you will get:

    x^2 - x - 15 = 0

    I'm confused because i thought the -15 would also have to divide by two...
    is it the book or am i missing something serious here?
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  2. #2
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    Quote Originally Posted by david18 View Post
    2x^2 - 2x -15 = 0
    Then it tells me to divide the equation by 2 and says when you divide the equation by 2 you will get:
    x^2 - x - 15 = 0
    I'm confused because i thought the -15 would also have to divide by two...
    You are correct. It should -15/2.
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  3. #3
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    Hello, David!

    I agree with Plato . . . it should be -\frac{15}{2}


    I wondered WHY they divided by 2 . . . Why not apply the Quadratic Formula now?

    Then I remembered some criticism I received in the past.


    [rant]

    A number of people insist on completing-the-square for every quadratic equation.

    Their argument: "I'd rather have my students understand the process
    . . rather than memorize bunch of formulas."
    What a crock!

    I'm all for Understanding . . . but learning a new formula is not evil.

    And certainly, after going through the derivation of the Quadratic Formula,
    . . we're entitled to use it, aren't we?


    Would you throw out the Binomial Theorem and Pascal's Triangle
    . . because you'd rather have your students do all the multiplication
    . . for, say, (a + b)^8 ? . I bet you would.
    But would you do it the long way? . . . I think not.

    No wonder 99% of the population hates Math.
    Some teachers think: "Suffering and Pain is a good thing; it makes you stronger."
    But I bet they have a bottle of aspirin in their bathroom.

    [/rant]
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  4. #4
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    Quote Originally Posted by Soroban View Post
    [size=3]

    I wondered WHY they divided by 2 . . . Why not apply the Quadratic Formula now?

    ...
    Hello, Soroban,

    If you divide the quadratic equation
    ax^2+bx+c=0 by a you get the quadratic equation in normal form:
    x^2+\frac{b}{a}x+\frac{c}{a}=0. using variables for the fractions:
    x^2+px+q=0. Then the quadratic formula reduces to:

    x_{1,2}=-\frac{p}{2} \pm \sqrt{\frac{p^2}{4} - q}

    That's the method which is taught in Germany - but how this method crossed the Atlantic Ocean I actually don't know.
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