Solve x^2=2x^2/4-8

$$x ^ { 2 } = \frac { 2 x ^ { 2 } } { 4 } - 8$$

Solve for x (complex solution)

$$x=-4i$$

$$x=4i$$

Steps by Finding Square Root

Multiply both sides of the equation by 4.

$$4x^{2}=2x^{2}-32$$

Subtract 2x^{2} from both sides.

$$4x^{2}-2x^{2}=-32$$

Combine 4x^{2} and -2x^{2} to get 2x^{2}.

$$2x^{2}=-32$$

Divide both sides by 2.

$$x^{2}=\frac{-32}{2}$$

Divide -32 by 2 to get -16.

$$x^{2}=-16$$

The equation is now solved.

$$x=4i x=-4i$$

Steps Using the Quadratic Formula

Multiply both sides of the equation by 4.

$$4x^{2}=2x^{2}-32$$

Subtract 2x^{2} from both sides.

$$4x^{2}-2x^{2}=-32$$

Combine 4x^{2} and -2x^{2} to get 2x^{2}.

$$2x^{2}=-32$$

Add 32 to both sides.

$$2x^{2}+32=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and 32 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\times 32}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\times 32}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\times 32}}{2\times 2}$$

Multiply -8 times 32.

$$x=\frac{0±\sqrt{-256}}{2\times 2}$$

Take the square root of -256.

$$x=\frac{0±16i}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±16i}{4}$$

Now solve the equation x=\frac{0±16i}{4} when ± is plus.

$$x=4i$$

Now solve the equation x=\frac{0±16i}{4} when ± is minus.

$$x=-4i$$

The equation is now solved.

$$x=4i x=-4i$$