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# Find the sum

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Intern
Joined: 25 Nov 2017
Posts: 1

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25 Nov 2017, 10:07
Find the sum of all solutions of
3|2 − x|^2 − 7|x − 2| =6

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5282
GMAT 1: 800 Q59 V59
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28 Nov 2017, 10:16
Nawarashraf wrote:
Find the sum of all solutions of
3|2 − x|^2 − 7|x − 2| =6

Posted from my mobile device

$$3|2 − x|^2 − 7|x − 2| = 6$$
$$3|x-2|^2 - 7|x-2| - 6 = 0$$
$$(3|x-2|+2)(|x-2|-3) = 0$$
$$3|x-2| + 2 = 0$$ or $$|x-2| = 3$$.
Since we have $$|x-2|≥0$$ and $$3|x-2| + 2≥2>0$$, $$3|x-2| + 2 ≠ 0$$.

From $$|x-2| = 3$$, we have $$x - 2 = ±3$$.
$$x = 2 ± 3$$.
$$x = 5$$ or $$-1$$.
Thus the sum of solutions is $$5 + (-1) = 4$$.
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Re: Find the sum   [#permalink] 28 Nov 2017, 10:16
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