Solve 2(3x-5)^2+32=0

$$2 ( 3 x - 5 ) ^ { 2 } + 32 = 0$$

Solve for x (complex solution)

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

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

Steps by Finding Square Root

Subtracting 32 from itself leaves 0.

$$2\left(3x-5\right)^{2}=-32$$

Divide both sides by 2.

$$\frac{2\left(3x-5\right)^{2}}{2}=-\frac{32}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$\left(3x-5\right)^{2}=-\frac{32}{2}$$

Divide -32 by 2.

$$\left(3x-5\right)^{2}=-16$$

Take the square root of both sides of the equation.

$$3x-5=4i 3x-5=-4i$$

Add 5 to both sides of the equation.

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

Subtracting -5 from itself leaves 0.

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

Subtract -5 from 4i.

$$3x=5+4i$$

Subtract -5 from -4i.

$$3x=5-4i$$

Divide both sides by 3.

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

Dividing by 3 undoes the multiplication by 3.

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

Divide 5+4i by 3.

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

Divide 5-4i by 3.

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

The equation is now solved.

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