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Math Help - solving quadratics by factoring, S-R, or completing the square

  1. #1
    Newbie dmanflynn's Avatar
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    solving quadratics by factoring, S-R, or completing the square

    hello, i need some one to help me through this problem, there are more but i figure if you work me through this one i should be able to get the others, but then agian i might find myself back here later tonight:-). I know i should probable not be asking to solve such a simple equation as this but i have my reasons. x^2+2x=5 i need to know which method ( factoring, square roots, or completing the square. ) and why and how to solve it that way. thanks a bunch in advance
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  2. #2
    MHF Contributor red_dog's Avatar
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    x^2+2x=5\Leftrightarrow x^2+2x+1-6=0\Leftrightarrow (x+1)^2-6=0\Leftrightarrow(x+1-\sqrt{6})(x+1+\sqrt{6})=0
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  3. #3
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    I got that it could not be factorable?
    oops, nvmd. i dont know the square root technique
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  4. #4
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    I always look at the discriminant in the quadratic equation.

    b^2 - 4ac

    Obviously if you have a negative value it will have complex roots.

    If the value is positive AND a square number - factorising is usually a suitable method.

    If the value is positive but NOT a square number - you should be looking to use the quadratic formula (plus you've already done a bit of it

    If the value is 0 - you have a repeated root so completing square would be best.

    In your example:

    a=1

    b=2

    c=-5

    Therefore 2^2 - (4*1*-5) = 24<br />

    So I would suggest you use the quadratic formula - which considering the solution has a root component is a good move.
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    ^^ agreed! i forgot about QF
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    Quote Originally Posted by dmanflynn View Post
    x^2+2x=5 i need to know which method ( factoring, square roots, or completing the square. ) and why and how to solve it that way. thanks a bunch in advance
    The technique you choose is up to you!

    In this particular case, the Quadratic Formula would probably be the simplest method. To review the methods and how to recognize when which method would be preferable, try here.
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  7. #7
    Newbie dmanflynn's Avatar
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    ok i think i got that one guys a big thanks to ya! how would i go about 3x^2=108?
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  8. #8
    Newbie dmanflynn's Avatar
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    guys if any body sees this again and can help please do! i gota have this done like pronto before tommarow i know i know its sunday why didnt you do it before? yeah well i get so freakin frustrated with it i get to the point i say screw it cause i cant get any body to explain some of the stuff in terms i can understand the problem i asked previously about i got but now i have another i need help with. thanks alot i know i seem like a noob but noobs need help too :-)
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    Quote Originally Posted by dmanflynn View Post
    ok i think i got that one guys a big thanks to ya! how would i go about 3x^2=108?
    The simplest method here would likely be to do the obvious division, and then solve by square roots.
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  10. #10
    Newbie dmanflynn's Avatar
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    Exclamation

    before anything would i get 3x^2-108=0? then id get x^2-36=0, then add (-18)^2 to both sides?
    would the answer be............... x=324 +- square root of 324? how do u simplify that, 2*2*3*3*3*3=324 just dont know how to simplify
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