Solve -8(x-3)^2=27

$$- 8 ( x - 3 ) ^ { 2 } = 27$$

Solve for x (complex solution)

$$x=-\frac{3\sqrt{6}i}{4}+3\approx 3-1.837117307i$$

$$x=\frac{3\sqrt{6}i}{4}+3\approx 3+1.837117307i$$

Steps by Finding Square Root

Dividing by -8 undoes the multiplication by -8.

$$\left(x-3\right)^{2}=\frac{27}{-8}$$

Divide 27 by -8.

$$\left(x-3\right)^{2}=-\frac{27}{8}$$

Take the square root of both sides of the equation.

$$x-3=\frac{3\sqrt{6}i}{4} x-3=-\frac{3\sqrt{6}i}{4}$$

Add 3 to both sides of the equation.

$$x-3-\left(-3\right)=\frac{3\sqrt{6}i}{4}-\left(-3\right) x-3-\left(-3\right)=-\frac{3\sqrt{6}i}{4}-\left(-3\right)$$

Subtracting -3 from itself leaves 0.

$$x=\frac{3\sqrt{6}i}{4}-\left(-3\right) x=-\frac{3\sqrt{6}i}{4}-\left(-3\right)$$

Subtract -3 from \frac{3i\sqrt{6}}{4}.

$$x=\frac{3\sqrt{6}i}{4}+3$$

Subtract -3 from -\frac{3i\sqrt{6}}{4}.

$$x=-\frac{3\sqrt{6}i}{4}+3$$

The equation is now solved.

$$x=\frac{3\sqrt{6}i}{4}+3 x=-\frac{3\sqrt{6}i}{4}+3$$