# How do you solve #(x-2)^2=-3#?

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To solve the equation (x-2)^2 = -3, we first need to isolate the squared term. Taking the square root of both sides gives us two possibilities:

- (x-2) = √(-3)
- (x-2) = -√(-3)

Since the square root of a negative number is imaginary, both sides of the equation will result in complex numbers. However, it's important to remember that the square root of -1 is denoted as "i", the imaginary unit.

So, we rewrite the equation:

- (x-2) = √3 * i
- (x-2) = -√3 * i

Now, we solve for x:

- x = 2 + √3 * i
- x = 2 - √3 * i

Therefore, the solutions to the equation (x-2)^2 = -3 are x = 2 + √3 * i and x = 2 - √3 * i.

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