SOLUTION: Can you please tell me how to complete the square for 4x^2+25y^2-33x+50y-311=0

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Question 966683: Can you please tell me how to complete the square for 4x^2+25y^2-33x+50y-311=0
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

to complete the square for 4x%5E2%2B25y%5E2-33x%2B50y-311=0 first group x terms together and y terms together
%284x%5E2-33x%29%2B%2825y%5E2%2B50y%29-311=0

4%28x%5E2-%2833%2F4%29x%29%2B25%28y%5E2%2B2y%29-311=0...recall the square of difference %28a-b%29%5E2=a%5E2-2ab%2Bb%5E2=> so, we need to add and subtract b%5E2
4%28x%5E2-%2833%2F4%29x%2Bb%5E2%29-b%5E2%2B25%28y%5E2%2B2y%2Bb%5E2%29-b%5E2-311=0
...since for x variable we have a=1 and 2ab=33%2F4, we can calculate b
2ab=33%2F4
2%2A1b=33%2F4
b=33%2F8
we do same with y variable where a=1 and 2ab=2=>b=1
then our equation will be:


4%28x%5E2-%2833%2F8%29%29%5E2-%281089%2F16%29%2B25%28y%2B1%29%5E2-25-311=0



4%28x%5E2-%2833%2F4%29%29%5E2-%281089%2F16%29%2B25%28y%5E2%2B2y%2B2%5E2%29-%285376%2F16%29=0

4%28x-33%2F8%29%5E2%2B25%28y%2B1%29%5E2-6465%2F16=0

4%28x-33%2F8%29%5E2%2B25%28y%2B1%29%5E2=6465%2F16