Solve for real x the equation x=6[(x-2)^1/2-1].

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We have to solve the equation x = 6[(x-2)^1/2 - 1]

x = 6[(x-2)^1/2 - 1]

=> x = 6*( x - 2)^1/2 - 6

=> x + 6 = 6*( x - 2)^1/2

take the square of both the sides

=> x^2 + 36 + 12x = 36 ( x - 2)

=> x^2 + 36 + 12x - 36x + 72 = 0

=> x^2 - 24x + 108 = 0

=> x^2 - 18x - 6x + 108 = 0

=> x( x - 18) - 6( x - 18) = 0

=> (x - 6)(x - 18) = 0

Therefore x can take the values 6 and 18.

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