Nawarashraf wrote:

Find the sum of all solutions of

3|2 − x|^2 − 7|x − 2| =6

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\(3|2 − x|^2 − 7|x − 2| = 6\)

\(3|x-2|^2 - 7|x-2| - 6 = 0\)

\((3|x-2|+2)(|x-2|-3) = 0\)

\(3|x-2| + 2 = 0\) 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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