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When the expression -2x^2-20x-53 is written in the form a(x+d)^2+e, where a, d, and e are constants, then what is the sum a+d+e?

 Dec 26, 2018
edited by Guest  Dec 26, 2018
 #1
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When the expression -2x^2-20x-53 is written in the form a(x+d)^2+e, where a, d, and e are constants, then what is the sum a+d+e?

 

 

-2x^2 - 20x - 53     factor out the -2

 

-2 (x^2 + 10x + 53/2 )

 

Take 1/2 of 10 = 5...square it = 25.....add and subtract it within the parentheses

 

-2 (x^2 + 10x + 25  +  53/2 - 25 )     factor the first 3 terms in the parentheses.....

 

-2 [ (x + 5)^2    + 53/2 - 50/2 ]

 

-2  [ (x + 5)^2 +  3/2 ]         apply the -2 across the terms in the parentheses

 

-2 (x + 5)^2  - 3

 

a = - 2

d = 5

e = -3

 

And their sum  is   0   !!!

 

 

 

cool cool cool

 Dec 26, 2018

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