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The quadratic -6x^2 + 30x - 216  can be written in the form a(x + b)^2 + c, where a, b, and c are constants. What is a+b+c?

 Dec 23, 2020
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-6x^2  + 30x - 216      factor out the  -6

 

-6  (x^2  - 5x  +  36)     complete the square on x

 

Take 1/2 of 5  = 5/2......square it  = 25/4     add and subtract this within the parentheses

 

-6 ( x^2  - 5x  +  25/4 +  36  - 25/4)        factor  the first three terms....simplify the rest

 

-6 [ (x - 5/2)^2  + 119/4 ]      distribute the  -6  acroos the terms in the  brackets

 

-6 (x  -5/2)^2  -357/2

 

a  =  -6     b  =  -5/2      c  =  -357/2

 

a  +  b  +  c    =   -  (12/2  + 5/2  + 357/2)   = - (374/2)  = -187

 

 

cool cool cool

 Dec 23, 2020

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