Solve 2x(x+1)-4x(x-2)-2x=x-4

$$2 x ( x + 1 ) - 4 x ( x - 2 ) - 2 x = x - 4$$

Solve for x

$$x=4$$

$$x=-\frac{1}{2}=-0.5$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x by x+1.

$$2x^{2}+2x-4x\left(x-2\right)-2x=x-4$$

Subtract x from both sides.

$$2x^{2}+2x-4x\left(x-2\right)-2x-x=-4$$

Combine -2x and -x to get -3x.

$$2x^{2}+2x-4x\left(x-2\right)-3x=-4$$

Add 4 to both sides.

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

Use the distributive property to multiply -4x by x-2.

$$2x^{2}+2x-4x^{2}+8x-3x+4=0$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}+2x+8x-3x+4=0$$

Combine 2x and 8x to get 10x.

$$-2x^{2}+10x-3x+4=0$$

Combine 10x and -3x to get 7x.

$$-2x^{2}+7x+4=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 7 for b, and 4 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-7±\sqrt{7^{2}-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Square 7.

$$x=\frac{-7±\sqrt{49-4\left(-2\right)\times 4}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-7±\sqrt{49+8\times 4}}{2\left(-2\right)}$$

Multiply 8 times 4.

$$x=\frac{-7±\sqrt{49+32}}{2\left(-2\right)}$$

Add 49 to 32.

$$x=\frac{-7±\sqrt{81}}{2\left(-2\right)}$$

Take the square root of 81.

$$x=\frac{-7±9}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-7±9}{-4}$$

Now solve the equation x=\frac{-7±9}{-4} when ± is plus. Add -7 to 9.

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

Reduce the fraction \frac{2}{-4} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{2}$$

Now solve the equation x=\frac{-7±9}{-4} when ± is minus. Subtract 9 from -7.

$$x=-\frac{16}{-4}$$

Divide -16 by -4.

$$x=4$$

The equation is now solved.

$$x=-\frac{1}{2} x=4$$

Steps for Completing the Square

Use the distributive property to multiply 2x by x+1.

$$2x^{2}+2x-4x\left(x-2\right)-2x=x-4$$

Subtract x from both sides.

$$2x^{2}+2x-4x\left(x-2\right)-2x-x=-4$$

Combine -2x and -x to get -3x.

$$2x^{2}+2x-4x\left(x-2\right)-3x=-4$$

Use the distributive property to multiply -4x by x-2.

$$2x^{2}+2x-4x^{2}+8x-3x=-4$$

Combine 2x^{2} and -4x^{2} to get -2x^{2}.

$$-2x^{2}+2x+8x-3x=-4$$

Combine 2x and 8x to get 10x.

$$-2x^{2}+10x-3x=-4$$

Combine 10x and -3x to get 7x.

$$-2x^{2}+7x=-4$$

Divide both sides by -2.

$$\frac{-2x^{2}+7x}{-2}=-\frac{4}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{7}{-2}x=-\frac{4}{-2}$$

Divide 7 by -2.

$$x^{2}-\frac{7}{2}x=-\frac{4}{-2}$$

Divide -4 by -2.

$$x^{2}-\frac{7}{2}x=2$$

Divide -\frac{7}{2}, the coefficient of the x term, by 2 to get -\frac{7}{4}. Then add the square of -\frac{7}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-\frac{7}{2}x+\left(-\frac{7}{4}\right)^{2}=2+\left(-\frac{7}{4}\right)^{2}$$

Square -\frac{7}{4} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=2+\frac{49}{16}$$

Add 2 to \frac{49}{16}.

$$x^{2}-\frac{7}{2}x+\frac{49}{16}=\frac{81}{16}$$

Factor x^{2}-\frac{7}{2}x+\frac{49}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{7}{4}\right)^{2}=\frac{81}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{4}\right)^{2}}=\sqrt{\frac{81}{16}}$$

Simplify.

$$x-\frac{7}{4}=\frac{9}{4} x-\frac{7}{4}=-\frac{9}{4}$$

Add \frac{7}{4} to both sides of the equation.

$$x=4 x=-\frac{1}{2}$$