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

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

Solve for x

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

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

Steps by Finding Square Root

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$x^{2}-x-2=\left(1-x\right)\left(x+2\right)$$

Use the distributive property to multiply 1-x by x+2 and combine like terms.

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

Add x to both sides.

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

Combine -x and x to get 0.

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

Add 2 to both sides.

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

Add 2 and 2 to get 4.

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

Divide both sides by 2.

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

Divide 4 by 2 to get 2.

$$x^{2}=2$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$x^{2}-x-2=\left(1-x\right)\left(x+2\right)$$

Use the distributive property to multiply 1-x by x+2 and combine like terms.

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

Add x to both sides.

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

Combine -x and x to get 0.

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

Subtract 2 from both sides.

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

Subtract 2 from -2 to get -4.

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

Add x^{2} to both sides.

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

Combine x^{2} and x^{2} to get 2x^{2}.

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

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}.

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

Square 0.

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

Multiply -4 times 2.

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

Multiply -8 times -4.

$$x=\frac{0±\sqrt{32}}{2\times 2}$$

Take the square root of 32.

$$x=\frac{0±4\sqrt{2}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{2}}{4}$$

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

$$x=\sqrt{2}$$

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

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

The equation is now solved.

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