Question 339605
Find the coefficient next to the x term, -2/3 in your case
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take 1/2 of it :   {{{(1/2)*(-2/3)=-1/3}}}
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Square this term:  {{{(-1/3)^2=1/9}}}
this is the amount you must add (and subtract to keep it balanced)

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in your example:  {{{x^2-(2/3)x=x^2-(2/3)x+1/9-1/9=(x-1/3)^2-(1/9)}}}