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"Write the following expressions in the form $X^2 − A^2$ using the method of completing the square."

"1) $x^2 + 8x + 9$"

I don't understand how that can be, but I did try to do it, with no obvious next steps.

My solution:-

$x^2 + 8x + 16 -16 + 9$

$(x + 4)^2 - 7$

I completed the square, but how can I put that in the form $X^2 - A^2$?

  • 4
    Can you think of any numbers $A$ such that $A^2=7$?2012-03-04
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    Note that $X$ is not the same thing as $x$. (Yes, case matters!). So, we can let $X$ be $x+4$; that takes care of the "$X^2$" part. For the $A^2$ part, use Zev's hint.2012-03-04
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    I took the liberty of changing the $4x$ to $8x$ as the rest of the work seems to suggest you did, in fact, mean $8x$2012-03-04
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    @ArturoMagidin Oh, now I understand :) Thank you all!2012-03-04
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    If you understand, write out your understanding as an answer. If after a few days no one has pointed out any mistakes, you can accept your answer.2012-03-04
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    See this video for example for completing the square.2012-03-05

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