Solve (3x-1)^2=-4

$$( 3 x - 1 ) ^ { 2 } = - 4$$

Solve for x (complex solution)

$$x=\frac{1}{3}-\frac{2}{3}i\approx 0.333333333-0.666666667i$$

$$x=\frac{1}{3}+\frac{2}{3}i\approx 0.333333333+0.666666667i$$

Steps by Finding Square Root

Add 1 to both sides of the equation.

$$3x-1-\left(-1\right)=2i-\left(-1\right) 3x-1-\left(-1\right)=-2i-\left(-1\right)$$

Subtracting -1 from itself leaves 0.

$$3x=2i-\left(-1\right) 3x=-2i-\left(-1\right)$$

Subtract -1 from 2i.

$$3x=1+2i$$

Subtract -1 from -2i.

$$3x=1-2i$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{1+2i}{3} \frac{3x}{3}=\frac{1-2i}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{1+2i}{3} x=\frac{1-2i}{3}$$

Divide 1+2i by 3.

$$x=\frac{1}{3}+\frac{2}{3}i$$

Divide 1-2i by 3.

$$x=\frac{1}{3}-\frac{2}{3}i$$

The equation is now solved.

$$x=\frac{1}{3}+\frac{2}{3}i x=\frac{1}{3}-\frac{2}{3}i$$