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?

ma931 Dec 26, 2018

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Dec 26, 2018

#1**+1 **

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 !!!

CPhill Dec 26, 2018