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
What is the sum of all possible solutions of the equation \(|x + 4|^2 - 10|x + 4| = 24?\)
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
|x + 4|² - 10|x + 4| = 24Gmat_mission wrote: ↑Sun Sep 12, 2021 8:57 amWhat 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
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