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How do I complete the square and find out the third number in these trinomials?

9x2 - 6x ??
9y2 + 12y ??

angry

Shades  Dec 28, 2015

Best Answer 

 #1
avatar+78618 
+15

9x^2 - 6x     first, factor out the 9

 

9 [x^2 - (2/3)x ]       Now, inside the brackets, take 1/2 of the coefficient on x = (1/2)(2/3) = 1/3   ....square it .... (1/3)^2  = 1/9.......add this and subtract it.....so we have

 

9 [ x^2 -(2/3)x + 1/9  - 1/9]        factor the 1st three terms

 

9 [ ( x - 1/3)^2  - 1/9 ]               distribute the 9 back across everything

 

9(x - 1/3)^2 -  1

 

 

The second one is similar

 

9y^2 + 12y

 

9 [ y ^2 + (4/3)y]       ........         (1/2)(4/3)  = 2/3      ......(2/3)^2  = 4/9

 

9[ y^2 + (4/3)y + 4/9   - 4/9]  =

 

9 [ (y + 2/3)^2 - 4/9]  =

 

9(y + 2/3)^2 - 4

 

 

 

cool cool cool

CPhill  Dec 28, 2015
Sort: 

5+0 Answers

 #1
avatar+78618 
+15
Best Answer

9x^2 - 6x     first, factor out the 9

 

9 [x^2 - (2/3)x ]       Now, inside the brackets, take 1/2 of the coefficient on x = (1/2)(2/3) = 1/3   ....square it .... (1/3)^2  = 1/9.......add this and subtract it.....so we have

 

9 [ x^2 -(2/3)x + 1/9  - 1/9]        factor the 1st three terms

 

9 [ ( x - 1/3)^2  - 1/9 ]               distribute the 9 back across everything

 

9(x - 1/3)^2 -  1

 

 

The second one is similar

 

9y^2 + 12y

 

9 [ y ^2 + (4/3)y]       ........         (1/2)(4/3)  = 2/3      ......(2/3)^2  = 4/9

 

9[ y^2 + (4/3)y + 4/9   - 4/9]  =

 

9 [ (y + 2/3)^2 - 4/9]  =

 

9(y + 2/3)^2 - 4

 

 

 

cool cool cool

CPhill  Dec 28, 2015
 #2
avatar+466 
+5

Thank you! cool

Shades  Dec 28, 2015
 #3
avatar+78618 
+5

No prob, Shades.......!!!!

 

 

cool cool cool

CPhill  Dec 28, 2015
 #4
avatar+91001 
0

Great answer Chris :)

Melody  Dec 28, 2015
 #5
avatar+78618 
0

Thanks, Melody.......

 

 

 

cool cool cool

CPhill  Dec 28, 2015

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