Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By Phantasma

Math Help - How was this solved?

  1. #1
    Junior Member
    Joined
    Jul 2013
    From
    canada
    Posts
    35
    Thanks
    1

    How was this solved?

    The question asks me to determine the intersection 3x-y=11 and 3x2-y2 = 47 This is the given answer.

    y=3x-11

    3x2-(3x-11)2=47

    3x2 -9x2 +66x-121-47=0

    -6x2+ 66x - 168= 0

    x2 -11x +28 = 0

    ..... and so on


    The problem I'm having is in line 3. I'm not sure where the '66x' came from?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie Phantasma's Avatar
    Joined
    Jun 2013
    From
    United States of Hysteria
    Posts
    19
    Thanks
    6

    Re: How was this solved?

    Quote Originally Posted by Urpes View Post
    3x2-(3x-11)2=47
    (3x-11)^2=9x^2-(2 \cdot 11 \cdot 3)x+121=9x^2-66x+121.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2013
    From
    canada
    Posts
    35
    Thanks
    1

    Re: How was this solved?

    Quote Originally Posted by Phantasma View Post
    (3x-11)^2=9x^2-(2 \cdot 11 \cdot 3)x+121=9x^2-66x+121.
    Is there anyway you can explain this step by step.

    I can see that 3x squared = 9x2 and I see that -11 squared = 121, however I don't know where the (2 x 11 x 3)x came from :S

    Also in the given answer for the question it says that instead of 121 it's -121.. im so confused.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie Phantasma's Avatar
    Joined
    Jun 2013
    From
    United States of Hysteria
    Posts
    19
    Thanks
    6

    Re: How was this solved?

    3x^2-(3x-11)^2=47 \\ 3x^2-(3x-11)(3x-11)=47 \\ 3x^2-(9x^2 - 2(3\cdot 11)x+121)=47 \, (\text{Multiplying through the binomial expressions using the distributive property}) \\ 3x^2 -9x^2 + 66x - 121 = 47 \, (\text{Multiplying the expression in parenthesis by -1, using the distributive property again}) \\ (3-9)x^2+66x-(121+47)=-6x^2+66x-168=0 \, (\text{Combining like terms using associative property}) \\ \footnotesize{\left(x-\left(\frac{-66+\sqrt{66^2-4(-6)(-168)}}{2(-6)}\right)\right)\left(x-\left(\frac{-66-\sqrt{66^2-4(-6)(-168)}}{2(-6)}\right)\right)=0} \, (\text{Factoring}).

    Is this kind of what you wanted?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jul 2013
    From
    canada
    Posts
    35
    Thanks
    1

    Re: How was this solved?

    Yes thank you very much, I see how it was done now, however I highly doubt I will ever be able to do it myself on a test. I had to stare at this for a while and I'm still having trouble understanding it completely.

    Thank you though, I've definitely come as close to understanding it as I probably ever will.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,670
    Thanks
    298
    Awards
    1

    Re: How was this solved?

    Quote Originally Posted by Urpes View Post
    Yes thank you very much, I see how it was done now, however I highly doubt I will ever be able to do it myself on a test. I had to stare at this for a while and I'm still having trouble understanding it completely.

    Thank you though, I've definitely come as close to understanding it as I probably ever will.
    The problem you were having can be helped by reviewing the FOIL method. After that it's the quadratic equation. You can study them separately so divide and conquer!

    -Dan
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum