When the expression -2x^2 - 20x - 53 + 14x + 17 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?
+592 First let's simplify the expression:
-2x2 - 20x + 14x - 53 + 17
= -2x2 - 6x - 36
Now use completing squares to change it into the form a(x + d)2 + e:
\(-2x^2 - 6x - 36\)
\(= -2(x^2 + 3x + 18)\)
\(= -2(x^2 + 3x + 2.25 - 2.25 + 18) \)
\(= -2((x + 1.5)^2 + 15.75)\)
\(= -2(x + 1.5)^2 - 31.5\)
a + d + e = -2 + 1.5 + (-31.5)
= -0.5 - 31.5
= -32
