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Math Help - Completing the Square!

  1. #1
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    Completing the Square!

    I have a number of completing the square tasks that I need to complete however have no idea where I am heading ha!

    Could some one show me a step by step guide on completing the example below and then hopefully I will be able to apply this for the rest of the questions.

    4Q - 28Q + 59

    Thank-you
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  2. #2
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    (2Q)^2 - 2\times{2Q}\times{7} + (7)^2 + (...)

    Fill in the bracket.
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  3. #3
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    Quote Originally Posted by rooney View Post
    I have a number of completing the square tasks that I need to complete however have no idea where I am heading ha!

    Could some one show me a step by step guide on completing the example below and then hopefully I will be able to apply this for the rest of the questions.

    4Q - 28Q + 59

    Thank-you
    I'll show you those step which you can use with nearly every "Completing the square" problems:

    \begin{array}{l}4Q^2-28Q+59=4(Q^2-7Q)+59\\<br />
=4\left(Q^2-7Q+\left(\frac72 \right)^2-\left(\frac72 \right)^2\right)+59\\<br />
=4\left(\left(Q^2-7Q+\left(\frac72 \right)^2\right)-\left(\frac72 \right)^2\right)+59 \\ <br />
= 4(Q-\frac72)^2-7+59<br />
= (2Q-7)^2+52\end{array}

    1. Factor out the leading factor of the square from the variables.
    2. Divide the leading factor of the linear summand by 2 and suare it.
    3. Subtract this new square at once.
    4. The first 3 summands in the bracket are a complete square.
    5. Expand the bracket and collect the constants.
    6. Multiply the complete square by the square-root of the leading factor (why?)
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  4. #4
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    The answer should be

    (2Q - 7)^2 + 10
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  5. #5
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    Ha contradicting answers hey!

    I'm trying to work through a procedure i found on the internet so that I can derive the answer myself. Not having a great deal of luck at the mo but i'l get there hopefully
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  6. #6
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    Quote Originally Posted by sa-ri-ga-ma View Post
    The answer should be

    (2Q - 7)^2 + 10
    You are right! Thanks for spotting my mistake (I forgot to square the 7)

    Quote Originally Posted by rooney View Post
    Ha contradicting answers hey!

    ...
    Here comes the correct calculation:

    \begin{array}{l}<br />
= 4(Q-\frac72)^2-4 \cdot \frac{7^2}{2^2}+59<br />
= (2Q-7)^2+10\end{array}
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