GMATinsight wrote:
Bunuel wrote:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?
A. -20
B. -5
C. -4
D. 0
E. 20
Let, \(|x + 2| = a\)
i.e. equation \(|x + 2|^2 - 5|x + 2| = -6\) becomes \(a^2 - 5a = -6\)
i.e. \(a^2 - 5a +6 = 0\)
i.e. \(a = 3, 2\)
If \(a = 3 = |x + 2|\) then \(x = 1 or -5\)
If \(a = 2 = |x + 2|\) then \(x = 0 or -4\)
Product of all possible values of \(x = (1)*(-5)*(0)*(-4) = 0\)
Answer: Option D
Hey Insight,
Hope you're well.
In a question like this, why can't I multiply out the brackets to make a quadratic equation then solve for x? For example, once I multiplied and simplified the above, I deduced: x^2 + 4x - 5 = 0, where x = -5 or 1. Therefore, the answer would be -5.
May you point out the flaw in my reasoning please?
Thanks in advance.
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78% (01:19) correct 
