Solve 6x^2-xy^2+xy^2=-8

$$6 { x }^{ 2 } -x { y }^{ 2 } +x { y }^{ 2 } =-8$$

Solve for x

$$x=-\frac{2\sqrt{3}i}{3}\approx -0-1.154700538i$$

$$x=\frac{2\sqrt{3}i}{3}\approx 1.154700538i$$

Steps by Finding Square Root

Combine -xy^{2} and xy^{2} to get 0.

$$6x^{2}=-8$$

Divide both sides by 6.

$$x^{2}=\frac{-8}{6}$$

Reduce the fraction \frac{-8}{6} to lowest terms by extracting and canceling out 2.

$$x^{2}=-\frac{4}{3}$$

The equation is now solved.

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

Steps Using the Quadratic Formula

Add 8 to both sides.

$$6x^{2}-xy^{2}+xy^{2}+8=0$$

Combine -xy^{2} and xy^{2} to get 0.

$$6x^{2}+8=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 8 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 6\times 8}}{2\times 6}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 6\times 8}}{2\times 6}$$

Multiply -4 times 6.

$$x=\frac{0±\sqrt{-24\times 8}}{2\times 6}$$

Multiply -24 times 8.

$$x=\frac{0±\sqrt{-192}}{2\times 6}$$

Take the square root of -192.

$$x=\frac{0±8\sqrt{3}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±8\sqrt{3}i}{12}$$

Now solve the equation x=\frac{0±8\sqrt{3}i}{12} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{3}i}{12} when ± is minus.

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

The equation is now solved.

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

Solve for y

$$y\in \mathrm{C}$$

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