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Take the square root of the problem, it becomes x-6, then add 6 to both sides and voila x=6.

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No.

The correct way is to factorise (the difference of two squares)

x2 - 36 = (x - 6)*(x + 6) and that is as far as you can go.

The original question was an expression, NOT an equation. There cannot be a solution to an expression.

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