What is the sum of all possible solutions of the equation \(x + 4^2  10x + 4 = 24?\)
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 \(x + 4^2  10x + 4 = 24?\)
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x + 4²  10x + 4 = 24Gmat_mission wrote: ↑Sun Sep 12, 2021 8:57 amWhat is the sum of all possible solutions of the equation \(x + 4^2  10x + 4 = 24?\)
A. 16
B. 14
C. 12
D. 8
E. 6
Answer: D
Source: Magoosh
Let's simplify matters by using some usubstitution
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