Solve (9k-1)^2=-125

$$( 9 k - 1 ) ^ { 2 } = - 125$$

Solve for k

$$k=\frac{-5\sqrt{5}i+1}{9}\approx 0.111111111-1.242259987i$$

$$k=\frac{1+5\sqrt{5}i}{9}\approx 0.111111111+1.242259987i$$

Steps by Finding Square Root

Add 1 to both sides of the equation.

$$9k-1-\left(-1\right)=5\sqrt{5}i-\left(-1\right) 9k-1-\left(-1\right)=-5\sqrt{5}i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$9k=5\sqrt{5}i-\left(-1\right) 9k=-5\sqrt{5}i-\left(-1\right)$$

Subtract -1 from 5i\sqrt{5}.

$$9k=1+5\sqrt{5}i$$

Subtract -1 from -5i\sqrt{5}.

$$9k=-5\sqrt{5}i+1$$

Divide both sides by 9.

$$\frac{9k}{9}=\frac{1+5\sqrt{5}i}{9} \frac{9k}{9}=\frac{-5\sqrt{5}i+1}{9}$$

Dividing by 9 undoes the multiplication by 9.

$$k=\frac{1+5\sqrt{5}i}{9} k=\frac{-5\sqrt{5}i+1}{9}$$