SOLUTION: Can you explain to me how a constant is found to add to the binomial so that it becomes the perfect square? Example: x2(exponent) - 2/3x

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Question 339605: Can you explain to me how a constant is found to add to the binomial so that it becomes the perfect square?
Example: x2(exponent) - 2/3x
Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
Find the coefficient next to the x term, -2/3 in your case
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take 1/2 of it : %281%2F2%29%2A%28-2%2F3%29=-1%2F3
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Square this term: %28-1%2F3%29%5E2=1%2F9
this is the amount you must add (and subtract to keep it balanced)
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in your example: x%5E2-%282%2F3%29x=x%5E2-%282%2F3%29x%2B1%2F9-1%2F9=%28x-1%2F3%29%5E2-%281%2F9%29