Gmat_mission wrote: ↑Sun Sep 12, 2021 8:57 am
What is the sum of all possible solutions of the equation \(|x + 4|^2 - 10|x + 4| = 24?\)
A. -16
B. -14
C. -12
D. -8
E. -6
Answer:
D
Source: Magoosh
|x + 4|² - 10|x + 4| = 24
Let's simplify matters by using some
u-substitution
Let u =
|x + 4| and then replace
|x + 4| with u to get:
u² - 10u = 24
Subtract 24 from both sides to get:
u² - 10u - 24 = 0
Factor to get:
(u - 12)(u + 2) = 0
So,
u = 12 or
u = -2
Now let's replace
u with
|x + 4|.
This means that
|x + 4| = 12 or
|x + 4| = -2
If
|x + 4| = 12, then x =
8 or
-16
If
|x + 4| = -2, then there are NO SOLUTIONS, since
|x + 4| will always be greater than or equal to zero.
So, there are only 2 solutions: x =
8 and x =
-16
We're asked to find the SUM of all possible solutions
x =
8 + (
-16) =
-8
Answer: D
Cheers,
Brent
