Solve -2x*(x+1)+2x=14

$$-2x \times (x+1)+2x=14$$

Solve for x (complex solution)

$$x=-\sqrt{7}i\approx -0-2.645751311i$$

$$x=\sqrt{7}i\approx 2.645751311i$$

Steps by Finding Square Root

Use the distributive property to multiply -2x by x+1.

$$-2x^{2}-2x+2x=14$$

Combine -2x and 2x to get 0.

$$-2x^{2}=14$$

Divide both sides by -2.

$$x^{2}=\frac{14}{-2}$$

Divide 14 by -2 to get -7.

$$x^{2}=-7$$

The equation is now solved.

$$x=\sqrt{7}i x=-\sqrt{7}i$$

Steps Using the Quadratic Formula

Use the distributive property to multiply -2x by x+1.

$$-2x^{2}-2x+2x=14$$

Combine -2x and 2x to get 0.

$$-2x^{2}=14$$

Subtract 14 from both sides.

$$-2x^{2}-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 0 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-14\right)}}{2\left(-2\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-14\right)}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{0±\sqrt{8\left(-14\right)}}{2\left(-2\right)}$$

Multiply 8 times -14.

$$x=\frac{0±\sqrt{-112}}{2\left(-2\right)}$$

Take the square root of -112.

$$x=\frac{0±4\sqrt{7}i}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{0±4\sqrt{7}i}{-4}$$

Now solve the equation x=\frac{0±4\sqrt{7}i}{-4} when ± is plus.

$$x=-\sqrt{7}i$$

Now solve the equation x=\frac{0±4\sqrt{7}i}{-4} when ± is minus.

$$x=\sqrt{7}i$$

The equation is now solved.

$$x=-\sqrt{7}i x=\sqrt{7}i$$