Solve -3^3x^2=6

$$- 3 ^ { 3 } x ^ { 2 } = 6$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{2}i}{3}\approx -0-0.471404521i$$

$$x=\frac{\sqrt{2}i}{3}\approx 0.471404521i$$

Steps by Finding Square Root

Calculate 3 to the power of 3 and get 27.

$$-27x^{2}=6$$

Divide both sides by -27.

$$x^{2}=\frac{6}{-27}$$

Reduce the fraction \frac{6}{-27} to lowest terms by extracting and canceling out 3.

$$x^{2}=-\frac{2}{9}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Calculate 3 to the power of 3 and get 27.

$$-27x^{2}=6$$

Subtract 6 from both sides.

$$-27x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -27 for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-27\right)\left(-6\right)}}{2\left(-27\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-27\right)\left(-6\right)}}{2\left(-27\right)}$$

Multiply -4 times -27.

$$x=\frac{0±\sqrt{108\left(-6\right)}}{2\left(-27\right)}$$

Multiply 108 times -6.

$$x=\frac{0±\sqrt{-648}}{2\left(-27\right)}$$

Take the square root of -648.

$$x=\frac{0±18\sqrt{2}i}{2\left(-27\right)}$$

Multiply 2 times -27.

$$x=\frac{0±18\sqrt{2}i}{-54}$$

Now solve the equation x=\frac{0±18\sqrt{2}i}{-54} when ± is plus.

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

Now solve the equation x=\frac{0±18\sqrt{2}i}{-54} when ± is minus.

$$x=\frac{\sqrt{2}i}{3}$$

The equation is now solved.

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