SOLUTION: what term should be added to x^2-2/3x ? so its a perfect square trinomial?

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Question 84728: what term should be added to x^2-2/3x ? so its a perfect square trinomial?
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
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x%5E2-%282%2F3%29x
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Find the number that must be added to the given binomial to make it a perfect square
trinomial.
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As long as the multiplier of the x%5E2 term is 1, you can use the following method:
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Identify the multiplier of the x term. In this problem that multiplier is -2%2F3.
Divide that by 2. When you do, the answer is %28-2%2F3%29%2F2+=+-2%2F6+=+-1%2F3. Square this answer:
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%28-1%2F3%29%5E2=+%2B1%2F9
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Thats the answer. If you add 1%2F9 to the original binomial you get:
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x%5E2+-+%282%2F3%29%2Ax+%2B+1%2F9
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and this trinomial factors into %28x+-+%281%2F3%29%29%5E2
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Hope this helps. Remember that you need the multiplier of the x%5E2 term to be 1. Then
you divide the multiplier of the x by 2 and square it to find the constant that you
need to add to make the trinomial a perfect square.
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Hope this helps you to understand how to work this problem.