GMATprofessional21 wrote: ↑Wed Aug 05, 2020 7:44 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
|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
