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

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

Solve for x

$$x=\sqrt{3}\approx 1.732050808$$

$$x=-\sqrt{3}\approx -1.732050808$$

Steps by Finding Square Root

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

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

To find the opposite of 1-x, find the opposite of each term.

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

Subtract 1 from 2 to get 1.

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

Subtract x from both sides.

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

Combine x and -x to get 0.

$$x^{2}-2=1$$

Add 2 to both sides.

$$x^{2}=1+2$$

Add 1 and 2 to get 3.

$$x^{2}=3$$

Take the square root of both sides of the equation.

$$x=\sqrt{3} x=-\sqrt{3}$$

Steps Using the Quadratic Formula

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

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

To find the opposite of 1-x, find the opposite of each term.

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

Subtract 1 from 2 to get 1.

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

Subtract 1 from both sides.

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

Subtract 1 from -2 to get -3.

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -3 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)}}{2}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12}}{2}$$

Take the square root of 12.

$$x=\frac{0±2\sqrt{3}}{2}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{2} when ± is plus.

$$x=\sqrt{3}$$

Now solve the equation x=\frac{0±2\sqrt{3}}{2} when ± is minus.

$$x=-\sqrt{3}$$

The equation is now solved.

$$x=\sqrt{3} x=-\sqrt{3}$$