Carcass wrote:
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
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITIONGRE - Math Book |x + 4|² - 10|x + 4| = 24Let's simplify matters by using some
u-substitution Let u =
|x + 4| and then replace
|x + 4| with u to get:
u² - 10u = 24Subtract 24 from both sides to get:
u² - 10u - 24 = 0Factor to get:
(u - 12)(u + 2) = 0So,
u = 12 or
u = -2Now let's replace
u with
|x + 4|.
This means that
|x + 4| = 12 or
|x + 4| = -2If
|x + 4| = 12, then x =
8 or
-16If
|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 =
-16We're asked to find the SUM of all possible solutions
x =
8 + (
-16) =
-8Answer: D
Cheers,
Brent