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Thread: Quadratic formula

  1. #1
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    Exclamation Quadratic formula

    I need help getting the variable b by itself

    this is what i have so far but need help finishing it. If you could show step by step instructions that'd be great.
    (2a)(2a)
    2ax=-b +/- sqrt(b^2-4ac)
    +b +b
    (2ax+b)^2= +/-sqrt( b^2-4ac)^2
    (2ax+b)^2= b^2-4ac
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Quadratic formula

    If you are trying to take the quadratic formula and solve for $\displaystyle b$, it will be far simpler to take the quadratic from which the formula is derived, and solve that for $\displaystyle b$:

    $\displaystyle ax^2+bx+c=0$

    $\displaystyle bx=-(ax^2+c)$

    $\displaystyle b=-\frac{ax^2+c}{x}$
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  3. #3
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    Re: Quadratic formula

    I know t would be easier to do it that way but the question asks to go from the formula i posted but thanks!
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Quadratic formula

    Well, we can begin with the quadratic formula:

    $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

    $\displaystyle 2ax=-b\pm\sqrt{b^2-4ac}$

    $\displaystyle 2ax+b=\pm\sqrt{b^2-4ac}$

    $\displaystyle 4a^2x^2+4abx+b^2=b^2-4ac$

    $\displaystyle 4a^2x^2+4abx+4ac=0$

    With $\displaystyle a\ne0$ we have:

    $\displaystyle ax^2+bx+c=0$

    Now, follow my first post.
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