Solve (5k-1)^2=-27

$$( 5 k - 1 ) ^ { 2 } = - 27$$

Solve for k

$$k=\frac{-3\sqrt{3}i+1}{5}\approx 0.2-1.039230485i$$

$$k=\frac{1+3\sqrt{3}i}{5}\approx 0.2+1.039230485i$$

Steps by Finding Square Root

Add 1 to both sides of the equation.

$$5k-1-\left(-1\right)=3\sqrt{3}i-\left(-1\right) 5k-1-\left(-1\right)=-3\sqrt{3}i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$5k=3\sqrt{3}i-\left(-1\right) 5k=-3\sqrt{3}i-\left(-1\right)$$

Subtract -1 from 3i\sqrt{3}.

$$5k=1+3\sqrt{3}i$$

Subtract -1 from -3i\sqrt{3}.

$$5k=-3\sqrt{3}i+1$$

Divide both sides by 5.

$$\frac{5k}{5}=\frac{1+3\sqrt{3}i}{5} \frac{5k}{5}=\frac{-3\sqrt{3}i+1}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$k=\frac{1+3\sqrt{3}i}{5} k=\frac{-3\sqrt{3}i+1}{5}$$