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When the expression $3x^2-24x+55$ is written in the form $a(x+d)^2+e$, where $a$, $d$, and $e$ are constants, then what is the sum $a+d+e$?

 Jun 2, 2020
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Starting with  3x2 - 24x + 55

write it in the form  a(x + d)2 + e

 

We will need to complete the square and factor out a number ...

 

The number that we can factor out of the x2 term and the x term is 3:

    3x2 - 24x + 55

=  3(x2 - 8x) + 55

 

Now, we need to complete the square:

=  3(x2 - 8x + 16) + 55 - 48

 

Factor:

=  3(x - 4)2 + 7

 

Your turn ...

 Jun 2, 2020

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