Given that |x + 4|^2 - 10|x + 4| = 24 and we need to find the sum of all possible solutions of the equation

Assume |x+4| = A, we will first solve for A and then use the value of A to solve for |x+4|

=> \(A^2\) - 10A = 24
=> \(A^2\) - 10A - 24 = 0
=> \(A^2\) - 12A + 2A - 24 = 0
=> A*(A-12) + 2*(A-12) = 0
=> (A-12)*(A+2) = 0
=> A = -2, 12

Now, A = |x+4| => A ≥ 0 (as Absolute value of any number can never be negative)

=> Only possible value of A is 12

=> |x+4| = 12
=> x+4 = 12 or x+4 = -12
=> x = 12-4 = 8 or x = -12-4 = -16

=> Sum of all possible solutions of the equation = 8 + (-16) = -8

So, Answer will be D
Hope it helps!

Watch the following video to learn How to Solve Absolute Value Problems

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