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Solve for x (complex solution)
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\left(x-2\right)^{2}=-3
Subtracting 3 from itself leaves 0.
x-2=\sqrt{3}i x-2=-\sqrt{3}i
Take the square root of both sides of the equation.
x-2-\left(-2\right)=\sqrt{3}i-\left(-2\right) x-2-\left(-2\right)=-\sqrt{3}i-\left(-2\right)
Add 2 to both sides of the equation.
x=\sqrt{3}i-\left(-2\right) x=-\sqrt{3}i-\left(-2\right)
Subtracting -2 from itself leaves 0.
x=2+\sqrt{3}i
Subtract -2 from i\sqrt{3}.
x=-\sqrt{3}i+2
Subtract -2 from -i\sqrt{3}.
x=2+\sqrt{3}i x=-\sqrt{3}i+2
The equation is now solved.