Solve (x-6)^2+27=7

$$( x - 6 ) ^ { 2 } + 27 = 7$$

Solve for x (complex solution)

$$x=-2\sqrt{5}i+6\approx 6-4.472135955i$$

$$x=6+2\sqrt{5}i\approx 6+4.472135955i$$

Steps by Finding Square Root

Subtracting 27 from itself leaves 0.

$$\left(x-6\right)^{2}=7-27$$

Subtract 27 from 7.

$$\left(x-6\right)^{2}=-20$$

Take the square root of both sides of the equation.

$$x-6=2\sqrt{5}i x-6=-2\sqrt{5}i$$

Add 6 to both sides of the equation.

$$x-6-\left(-6\right)=2\sqrt{5}i-\left(-6\right) x-6-\left(-6\right)=-2\sqrt{5}i-\left(-6\right)$$

Subtracting -6 from itself leaves 0.

$$x=2\sqrt{5}i-\left(-6\right) x=-2\sqrt{5}i-\left(-6\right)$$

Subtract -6 from 2i\sqrt{5}.

$$x=6+2\sqrt{5}i$$

Subtract -6 from -2i\sqrt{5}.

$$x=-2\sqrt{5}i+6$$

The equation is now solved.

$$x=6+2\sqrt{5}i x=-2\sqrt{5}i+6$$