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Math Help - Please help with these Quadratic Equations

  1. #1
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    Please help with these Quadratic Equations

    Any chance i can have a step by step demo of these. thanks.

    -x + 8X - 15 = 0


    6x^2 - 17x + 5 = 0


    -3b^2 - 26b = -9

    Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Brownhash View Post
    Any chance i can have a step by step demo of these. thanks.

    -x^2 + 8X - 15 = 0


    6x^2 - 17x + 5 = 0


    -3b^2 - 26b = -9

    Thanks
    It should be squared...right?

    For the first one, get rid of the negative sign in front of x^2:

    -(x^2-8x+15)=0 \implies (x-3)(x-5)=0 \implies {\color{red}\boxed{x=3}} \ \text{or} {\color{red}\boxed{x=5}}.

    For the second one, use the quadratic formula:

    x=\frac{-(-17)\pm\sqrt{(-17)^2-4(6)(5)}}{2(6)}=\frac{17\pm\sqrt{169}}{12}=\frac{1  7\pm 13}{12}\implies {\color{red}\boxed{x=\frac{5}{2}}} \ \text{or} \ {\color{red}\boxed{x=\frac{1}{3}}}

    Try doing the last one yourself. I'd recommend that you divide through by -3 to clean things up a little bit!

    I hope this helped you out!
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  3. #3
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    Thankyou

    Thanks for the help there much appreciated.
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by Brownhash View Post
    Any chance i can have a step by step demo of these. thanks.

    -x + 8X - 15 = 0


    6x^2 - 17x + 5 = 0


    -3b^2 - 26b = -9

    Thanks

    Your second equation can be factored as well:

    6x^2-17x+5

    My technique:
    1. Multiply leading coef. times constant: 6 X 5 = 30
    2. Find factors of 30 that add up to -17. That woud be -15 and -2
    3. Replace -17x with these 2 factors.
    4. Factor by grouping

    Here goes:

    6x^2-15x-2x+5=0

    (6x^2-15x)-(2x+5)=0

    3x(2x-5)-1(2x-5)=0

    (3x-1)(2x-5)=0

    x=\frac{1}{3} \ or \ x=\frac{5}{2}
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  5. #5
    A riddle wrapped in an enigma
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    Your third equation can be factored as well:

    -3b^2-26b=-9

    -3b^2-26b+9=0

    Multiply by -1

    3b^2+26b-9=0

    My technique:
    1. Multiply leading coef. times constant: 3 X 9 = 27
    2. Find factors of 27 that add up to 26. That woud be -1 and 27
    3. Replace 26b with these 2 factors.
    4. Factor by grouping

    Here goes:

    3b^2+27b-b-9=0

    (3b^2+27b)-b-9=0

    3b(b+9)-1(b+9)=0

    (3b-1)(b+9)=0

    b=\frac{1}{3} \ or \ b=-9
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