Solve x-2=(x+1)x

$$x - 2 = ( x + 1 ) x$$

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

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

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

Subtract x^{2} from both sides.

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

Add 2 to both sides. Anything plus zero gives itself.

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

Divide both sides by -1.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

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

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

Subtract x^{2} from both sides.

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-1\right)\left(-2\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$x=\frac{0±\sqrt{4\left(-2\right)}}{2\left(-1\right)}$$

Multiply 4 times -2.

$$x=\frac{0±\sqrt{-8}}{2\left(-1\right)}$$

Take the square root of -8.

$$x=\frac{0±2\sqrt{2}i}{2\left(-1\right)}$$

Multiply 2 times -1.

$$x=\frac{0±2\sqrt{2}i}{-2}$$

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

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

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

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

The equation is now solved.

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