Results 1 to 8 of 8
Like Tree1Thanks
  • 1 Post By Caddym89

Math Help - Quadratic Equation help

  1. #1
    Newbie
    Joined
    Apr 2013
    From
    Sydney
    Posts
    17
    Thanks
    2

    Quadratic Equation help

    Hi there, I'm having trouble with two of the more challenging problems in my homework.

    1) 2x2 - 3x + 2a = 0 , this needs to be solved using complete the square method.

    2) c2x2 - x - 1 = x2, to be solved using quadratic formula.

    any help would be appreciated, thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member agentmulder's Avatar
    Joined
    Aug 2011
    From
    42nd parallel, North America
    Posts
    105
    Thanks
    33

    Re: Quadratic Equation help

    1) To complete a square isolate the constant term, multiply everything by 4 times the coeficient of x^2, square the coefficient of x and add it to both sides. It looks like this

     2x^2 - 3x = -2a

    multiply through by 4*2 = 8

     16x^2 - 24x = -16a

    add (-3)^2 = 9 to both sides

     16x^2 - 24x + 9 = 9 - 16a

    The square has been completed on the left.

    (4x - 3)^2 = 9 - 16a

    Take square root

     4x - 3 = \pm \sqrt{9 - 16a}

    add 3

     4x = 3 \pm \sqrt{9 - 16a}

    divide by 4

     x = \frac{3 \pm \sqrt{9 - 16a} }{4}

    2) To use the popular version of the quadratic formula set the equation to 0 then identify a, b, and c then plug into the formula.

    c^2x^2 - x^2 - x - 1 = 0

     (c^2 - 1)x^2 - x - 1 = 0

     If \ ax^2 + bx + c = 0

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

    a = c^2 - 1
    b = -1
    c = -1

    plug it in

     x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(c^2 - 1)(-1)}}{2(c^2 - 1)}

    Simplify.

    Last edited by agentmulder; April 9th 2013 at 10:28 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Apr 2013
    From
    Sydney
    Posts
    17
    Thanks
    2

    Re: Quadratic Equation help

    Cheers agentmulder!
    Thanks from agentmulder
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member agentmulder's Avatar
    Joined
    Aug 2011
    From
    42nd parallel, North America
    Posts
    105
    Thanks
    33

    Re: Quadratic Equation help

    Quote Originally Posted by Caddym89 View Post
    Cheers agentmulder!
    I'll drink to that!

    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    826
    Thanks
    209

    Re: Quadratic Equation help

    Quadratic Equation help-10-apr-13-2.png
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Member agentmulder's Avatar
    Joined
    Aug 2011
    From
    42nd parallel, North America
    Posts
    105
    Thanks
    33

    Re: Quadratic Equation help

    Quote Originally Posted by ibdutt View Post
    Click image for larger version. 

Name:	10-Apr 13-2.png 
Views:	8 
Size:	18.6 KB 
ID:	27885
    You can complete the square this way too...

     ax^2 + bx + c = 0

     ax^2 + bx = -c

     4a(ax^2 + bx) = -4ac

     4a^2x^2 + 4abx = -4ac

    add b^2 to both sides

     4a^2x^2 + 4abx + b^2 = b^2 - 4ac

     (2ax + b)^2 = b^2 - 4ac

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

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

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

    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294

    Re: Quadratic Equation help

    Quote Originally Posted by Caddym89 View Post
    Hi there, I'm having trouble with two of the more challenging problems in my homework.

    1) 2x2 - 3x + 2a = 0 , this needs to be solved using complete the square method.

    2) c2x2 - x - 1 = x2, to be solved using quadratic formula.

    any help would be appreciated, thanks.
    While I do like Agent Mulder's version of completing the square, the more common method is to take out whatever the a term is as a factor first and complete the square on the remaining stuff.

    \displaystyle \begin{align*} 2x^2 - 3x + 2a &= 0 \\ x^2 - \frac{3}{2} x + a &= 0 \\ x^2 - \frac{3}{2}x + \left( -\frac{3}{4} \right) ^2 - \left( -\frac{3}{4} \right) ^2 + a &= 0 \\ \left( x  - \frac{3}{4} \right) ^2 - \frac{9}{16} + \frac{16a}{16} &= 0 \\ \left( x - \frac{3}{4} \right) ^2 &= \frac{9 - 16a}{16} \\ x - \frac{3}{4} &= \frac{\pm \sqrt{ 9 - 16a }}{4} \\ x &= \frac{3 \pm \sqrt{ 9 - 16a }}{4}  \end{align*}
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Apr 2013
    From
    Sydney
    Posts
    17
    Thanks
    2

    Re: Quadratic Equation help

    Thanks everyone, it's useful to know more than one method of completing the square also. My problem is making silly mistakes, I was originally stuck on this trying to figure out how to get the 16a in prove it's method, this is again not so difficult. (;
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quadratic equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: June 6th 2010, 07:35 PM
  2. Replies: 3
    Last Post: April 25th 2010, 03:53 PM
  3. quadratic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 6th 2010, 10:13 PM
  4. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 16th 2010, 09:27 PM
  5. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: June 19th 2008, 10:28 AM

Search Tags


/mathhelpforum @mathhelpforum