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What is the sum of all possible values of k for which x^2 + kx - 9x + 25 + 4x + 11 is the square of a binomial?

 Jan 6, 2022
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Answer: 10

Explanation:

 

Simplifying that expression turns it into \(x^2+(k-5)x+36\). The 36 at the end (and the fact that the coefficent of x^2 is 1) shows us that there are only two possible options: (x+6)^2 and (x-6)^2. Expanding the first gives x^2 + 12x +36, while the second gives x^2-12x+36.

Set up an equation for the first one:

k-5=12

k=17

Set up an equation for the second one:

k-5=-12

k=-7

-7 + 17 = 10.

 Jan 6, 2022

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