Solve (x+2)(x-1)=2-3x

$$( x + 2 ) ( x - 1 ) = 2 - 3 x$$

Solve for x

$$x=2\sqrt{2}-2\approx 0.828427125$$

$$x=-2\sqrt{2}-2\approx -4.828427125$$

Steps Using the Quadratic Formula

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

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

Subtract 2 from both sides.

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

Subtract 2 from -2 to get -4.

$$x^{2}+x-4=-3x$$

Add 3x to both sides.

$$x^{2}+x-4+3x=0$$

Combine x and 3x to get 4x.

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

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

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

Square 4.

$$x=\frac{-4±\sqrt{16-4\left(-4\right)}}{2}$$

Multiply -4 times -4.

$$x=\frac{-4±\sqrt{16+16}}{2}$$

Add 16 to 16.

$$x=\frac{-4±\sqrt{32}}{2}$$

Take the square root of 32.

$$x=\frac{-4±4\sqrt{2}}{2}$$

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

$$x=\frac{4\sqrt{2}-4}{2}$$

Divide -4+4\sqrt{2} by 2.

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

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

$$x=\frac{-4\sqrt{2}-4}{2}$$

Divide -4-4\sqrt{2} by 2.

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

The equation is now solved.

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

Steps for Completing the Square

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

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

Add 3x to both sides.

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

Combine x and 3x to get 4x.

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

Add 2 to both sides.

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

Add 2 and 2 to get 4.

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

Divide 4, the coefficient of the x term, by 2 to get 2. Then add the square of 2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 2.

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

Add 4 to 4.

$$x^{2}+4x+4=8$$

Factor x^{2}+4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+2\right)^{2}=8$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+2\right)^{2}}=\sqrt{8}$$

Simplify.

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

Subtract 2 from both sides of the equation.

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