Solve x-2x-1+2x^2+x+2x+3-2x+2=0

$$x-2x-1+2 { x }^{ 2 } +x+2x+3-2x+2=0$$

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 x and -2x to get -x.

$$-x-1+2x^{2}+x+2x+3-2x+2=0$$

Combine -x and x to get 0.

$$-1+2x^{2}+2x+3-2x+2=0$$

Add -1 and 3 to get 2.

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

Combine 2x and -2x to get 0.

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

Add 2 and 2 to get 4.

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

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

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

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 x and -2x to get -x.

$$-x-1+2x^{2}+x+2x+3-2x+2=0$$

Combine -x and x to get 0.

$$-1+2x^{2}+2x+3-2x+2=0$$

Add -1 and 3 to get 2.

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

Combine 2x and -2x to get 0.

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

Add 2 and 2 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}.

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

Square 0.

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

Multiply -4 times 2.

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

Multiply -8 times 4.

$$x=\frac{0±\sqrt{-32}}{2\times 2}$$

Take the square root of -32.

$$x=\frac{0±4\sqrt{2}i}{2\times 2}$$

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.

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