Live GMAT classes with Target Test Prep start Nov 21 and Nov 22. First class free.
See classesLearn live with an expert or move at your own pace. Every option includes the complete TTP study system.
Target Test Prep was voted #1 Best Test Prep in the 2026 Newsweek Readers’ Choice™ Awards.
with Josh Braslow, 20+ years in test prep
Self-paced EA prep. Study on your schedule.
with
Complete access from day one. Study on your schedule.
We can write the equation as x² + 4x + 4 = |x + 2| ----> (x + 2)² = |x + 2|artstudent wrote:Is there a quicker way to do this problem than doing the cases for the absolute value?
What is the product of all the solutions of x^2+4x+7=|X+2|+3?
Anurag@Gurome wrote:We can write the equation as x² + 4x + 4 = |x + 2| ----> (x + 2)² = |x + 2|artstudent wrote:Is there a quicker way to do this problem than doing the cases for the absolute value?
What is the product of all the solutions of x^2+4x+7=|X+2|+3?
Now, (x + 2)² can be written as |x + 2|²
Hence, |x + 2|² = |x + 2|
---> |x + 2|² - |x + 2| = 0
---> |x + 2|(|x + 2| - 1) = 0
Thus, either |x + 2| = 0 or |x + 2| = 1
----> either x = -2 or x = -1 or x = -3
Hence, product of all the solutions = (-1)*(-2)*(-3) = -6
