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Math Help - Factorisation and Completing the Square

  1. #1
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    Factorisation and Completing the Square

    Maths is certainly not me, why on earth I decided to pick Further is beyond comprehension. A couple of questions have got me, eternal thanks for any response.

    1. Solve quadratic by factorising:

    y^2+8y=0


    2. Solve by completing the square:

    3x^2-5x-1=0


    Thanks in advance!
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Nick87 View Post
    1. Solve quadratic by factorising:

    y^2+8y=0
    What factor is common to both terms?


    Quote Originally Posted by Nick87 View Post
    2. Solve by completing the square:

    3x^2-5x-1=0
    3x^2 - 5x - 1 = 0

    x^2 - \frac{5}{3}x - \frac{1}{3} = 0

    x^2 - \frac{5}{3}x = \frac{1}{3}

    Now, you have this equation and the left hand side is in the form of
    x^2 + 2bx

    By comparison we get that 2b = -\frac{5}{3} \implies b = -\frac{5}{6}.

    We want to add something to x^2 + 2bx that will make it a perfect square. If you look at the formula (a + b)^2 = a^2 + 2ab + b^2 you will see that if we add a b^2 to the two terms we get
    x^2 + 2bx + b^2 = (x + b)^2

    So we want to add a b^2 = \frac{25}{36} to both sides of the equation:
    x^2 - \frac{5}{3}x + \frac{25}{36} = \frac{1}{3} + \frac{25}{36}

    So...

    \left ( x - \frac{5}{6} \right ) ^2 = \frac{37}{36}

    Can you finish it from here?

    -Dan
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  3. #3
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    Krizalid's Avatar
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    Or for the second one:

    \begin{aligned}3x^2  - 5x - 1 &=0\\ 36x^2  - 60x - 12 &=0\\ (6x - 5)^2  &= 37.\end{aligned}

    Dan's answer is in agreement with mine.
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