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Math Help - Quadratic Equations, Exam Tommorow.

  1. #1
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    Quadratic Equations, Exam Tommorow.

    I have a few problems that I'm trying to understand. If anyone can assist me that would be greatly appreciated.

    Solve by using square root property:
    1) 3(x-4)^2 = 15
    2) (3x-4)^2 = 8


    Solve by completing the square:
    3) 2x^2 - 7x + 3= 0


    Solve using the Quadratic Formula:
    4) 3x^2 - 3x - 4= 0



    Thank you.
    Last edited by FactoringAnguish; November 18th 2007 at 04:53 PM.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by FactoringAnguish View Post
    I have a few problems that I'm trying to understand. If anyone can assist me that would be greatly appreciated.

    Solve by using square root property:
    1) 3(x-4)^2 = 15
    2) (3x-4)^2 = 8
    i'll do 1, do number 2..

    3(x-4)^2 = 15 \implies (x-4)^2 = 5 \implies \sqrt {(x-4)^2} = \sqrt 5

    \implies |x-4| = \sqrt 5 \implies x - 4 = \pm \sqrt 5 \implies x = 4 \pm \sqrt 5


    Quote Originally Posted by FactoringAnguish View Post

    Solve by completing the square:
    3) 2x^2 - 7x + 3= 0
    2x^2 - 7x + 3 = 0 \implies x^2 - \frac{7}{2}x + \frac{3}{2} = 0

    \implies x^2 - \frac{7}{2}x = - \frac{3}{2} adding \frac{49}{16} sides, we have x^2 - \frac{7}{2}x + \frac{49}{16} = \frac{49}{16} - \frac{3}{2}

    \implies \left( {x-\frac{7}{4}} \right) ^2 = \frac{25}{16} \implies \left( {x-\frac{7}{4}} \right) = \pm \frac{5}{4}

    from here, continue.. just like in number 1.

    Quote Originally Posted by FactoringAnguish View Post
    Solve using the Quadratic Formula:
    4) 3x^2 - 3x - 4= 0

    Thank you.
    if we have a quadratic poly of the form ax^2 + bx + c = 0, then x= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

    so, a= 3, b= -3, c = -4.. do the substitution..
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  3. #3
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    Thanks, makes perfect sense now that I see it worked out
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  4. #4
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    Methods for solving quadratics

    Quote Originally Posted by FactoringAnguish View Post
    I have a few problems that I'm trying to understand. If anyone can assist me that would be greatly appreciated.

    Solve by using square root property:
    1) 3(x-4)^2 = 15
    2) (3x-4)^2 = 8


    Solve by completing the square:
    3) 2x^2 - 7x + 3= 0


    Solve using the Quadratic Formula:
    4) 3x^2 - 3x - 4= 0



    Thank you.
    You can get step by step help on solving any quadratic equation you want by factoring, completing the square, extracting square roots, and the quadratic formula at:

    Free Online Quadratic Equation Solver: Solve by Factoring (or Factoring by Grouping)

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