Solve 4x-6-2x^2-4x-6=-8

$$4 x - 6 - 2 x ^ { 2 } - 4 x - 6 = - 8$$

Solve for x (complex solution)

$$x=-\sqrt{2}i\approx -0-1.414213562i$$

$$x=\sqrt{2}i\approx 1.414213562i$$

Steps by Finding Square Root

Combine 4x and -4x to get 0.

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

Subtract 6 from -6 to get -12.

$$-12-2x^{2}=-8$$

Add 12 to both sides.

$$-2x^{2}=-8+12$$

Add -8 and 12 to get 4.

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

Divide both sides by -2.

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

Divide 4 by -2 to get -2.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Combine 4x and -4x to get 0.

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

Subtract 6 from -6 to get -12.

$$-12-2x^{2}=-8$$

Add 8 to both sides.

$$-12-2x^{2}+8=0$$

Add -12 and 8 to get -4.

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

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.

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

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

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

Square 0.

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

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-4\right)}}{2\left(-2\right)}$$

Multiply 8 times -4.

$$x=\frac{0±\sqrt{-32}}{2\left(-2\right)}$$

Take the square root of -32.

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

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{2}i}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{2}i}{-4} when ± is plus.

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

Now solve the equation x=\frac{0±4\sqrt{2}i}{-4} when ± is minus.

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

The equation is now solved.

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