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Find the solution of the equation |x - 2|^2 + |x - 2| − 6 = 0.

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Find the solution of the equation |x - 2|2 + |x - 2| − 6 =  0.

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 We have

|x - 2|2 + |x - 2| − 6 =  0.

Let | x - 2| = X. Now,

X2 + X - 6 = 0.

Therefore, |x - 2| = 2 and |x - 2| = -3.

Now,|x - 2| = -3.= -3 is not possible.

So    x − 2 = 2 or x − 2 =  -2

Therefore, x = 4 or x = 0.

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