Solve -2(3x+4)^2-5=45

$$- 2 ( 3 x + 4 ) ^ { 2 } - 5 = 45$$

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

Subtracting 5 from itself leaves 0.

$$-2\left(3x+4\right)^{2}=45+5$$

Add 45 to 5.

$$-2\left(3x+4\right)^{2}=50$$

Divide both sides by -2.

$$\frac{-2\left(3x+4\right)^{2}}{-2}=\frac{50}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$\left(3x+4\right)^{2}=\frac{50}{-2}$$

Divide 50 by -2.

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

Take the square root of both sides of the equation.

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

Subtract 4 from both sides of the equation.

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

Subtracting 4 from itself leaves 0.

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

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.

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