Solve x(-1/2)x=6

$$x ( - \frac { 1 } { 2 } ) x = 6$$

Solve for x (complex solution)

$$x=-2\sqrt{3}i\approx -0-3.464101615i$$

$$x=2\sqrt{3}i\approx 3.464101615i$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$x^{2}\left(-\frac{1}{2}\right)=6$$

Multiply both sides by -2, the reciprocal of -\frac{1}{2}.

$$x^{2}=6\left(-2\right)$$

Multiply 6 and -2 to get -12.

$$x^{2}=-12$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$x^{2}\left(-\frac{1}{2}\right)=6$$

Subtract 6 from both sides.

$$x^{2}\left(-\frac{1}{2}\right)-6=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-\frac{1}{2}x^{2}-6=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -\frac{1}{2} for a, 0 for b, and -6 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1}{2}\right)\left(-6\right)}}{2\left(-\frac{1}{2}\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1}{2}\right)\left(-6\right)}}{2\left(-\frac{1}{2}\right)}$$

Multiply -4 times -\frac{1}{2}.

$$x=\frac{0±\sqrt{2\left(-6\right)}}{2\left(-\frac{1}{2}\right)}$$

Multiply 2 times -6.

$$x=\frac{0±\sqrt{-12}}{2\left(-\frac{1}{2}\right)}$$

Take the square root of -12.

$$x=\frac{0±2\sqrt{3}i}{2\left(-\frac{1}{2}\right)}$$

Multiply 2 times -\frac{1}{2}.

$$x=\frac{0±2\sqrt{3}i}{-1}$$

Now solve the equation x=\frac{0±2\sqrt{3}i}{-1} when ± is plus.

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

Now solve the equation x=\frac{0±2\sqrt{3}i}{-1} when ± is minus.

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

The equation is now solved.

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