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FACTORISING, which type do i use, when to find value of x and when to not?? watch

    • Thread Starter

    You're correct! Looking back through all my wokring i seemed to have made the stupid mistake of 3x x 8=28x instead of 24x ! :doh: Thanks for your help everyone!
    (Original post by Notnek)
    You should get 0 = 14x^2 - 41x - 3.

    Have another go and please post all your working if you get stuck. Also, for future questions please always post the original question and your full attempt.

    Okay we have:

     Ax^{2}  + Bx + C = 0.

    As others have stated, we have methods of finding values of x including:
    - Quadratic equation,

    - Completing the square.

    However, as we have some large values we can try inspection.


    For inspection, we could try  (kx + l) (mx + n) \, = \, (km)x^{2} + (lm+kn)x + ln.

    We need:

    - ln = C

    - lm +kn = B,

    - km = A.


    For your equation:  14x^{2} - 41x - 3,

    Try:  (14x + a)(x+b) .

    We need:

    - ab = -3, (a=-1 and b = 3 ? or a=1 and b = -3 ? or a=3 and b=-1 ? ...)

    - a + 14b = -41.

    Are you able to carry on from here?

    Another method you can try (learned this here on TSR) is:

     14x^{2} - 41x - 3.

    Multiply by the coefficient of  x^{2} :

     (14)14x^{2} - (14)41x - (14)3,

    Let  z = 14x :

     z^{2} - 41z - 42 .

    Then factorise (remembering to divide by 14 at the end).

    Are you able to carry on with this?
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