Solve left(3x-4right)^2=-25

$${ \left(3x-4 \right) }^{ 2 } =-25$$

Solve for x (complex solution)

$$x=\frac{4}{3}-\frac{5}{3}i\approx 1.333333333-1.666666667i$$

$$x=\frac{4}{3}+\frac{5}{3}i\approx 1.333333333+1.666666667i$$

Steps by Finding Square Root

Add 4 to both sides of the equation.

$$3x-4-\left(-4\right)=5i-\left(-4\right) 3x-4-\left(-4\right)=-5i-\left(-4\right)$$

Subtracting -4 from itself leaves 0.

$$3x=5i-\left(-4\right) 3x=-5i-\left(-4\right)$$

Subtract -4 from 5i.

$$3x=4+5i$$

Subtract -4 from -5i.

$$3x=4-5i$$

Divide both sides by 3.

$$\frac{3x}{3}=\frac{4+5i}{3} \frac{3x}{3}=\frac{4-5i}{3}$$

Dividing by 3 undoes the multiplication by 3.

$$x=\frac{4+5i}{3} x=\frac{4-5i}{3}$$

Divide 4+5i by 3.

$$x=\frac{4}{3}+\frac{5}{3}i$$

Divide 4-5i by 3.

$$x=\frac{4}{3}-\frac{5}{3}i$$

The equation is now solved.

$$x=\frac{4}{3}+\frac{5}{3}i x=\frac{4}{3}-\frac{5}{3}i$$