Solve -4-2x^2=-2

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

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Add 4 to both sides.

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

Add -2 and 4 to get 2.

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

Divide both sides by -2.

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

Divide 2 by -2 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Add 2 to both sides.

$$-4-2x^{2}+2=0$$

Add -4 and 2 to get -2.

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

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.

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

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

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

Square 0.

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

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-2\right)}}{2\left(-2\right)}$$

Multiply 8 times -2.

$$x=\frac{0±\sqrt{-16}}{2\left(-2\right)}$$

Take the square root of -16.

$$x=\frac{0±4i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4i}{-4}$$

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

$$x=-i$$

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

$$x=i$$

The equation is now solved.

$$x=-i x=i$$