Solve -2x(x-1)=0

$$-2x(x-1)=0$$

Solve for x

$$x=1$$

$$x=0$$

Steps Using Factoring

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

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

Factor out x.

$$x\left(-2x+2\right)=0$$

To find equation solutions, solve x=0 and -2x+2=0.

$$x=0 x=1$$

Steps Using the Quadratic Formula

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

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

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

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

Take the square root of 2^{2}.

$$x=\frac{-2±2}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-2±2}{-4}$$

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

$$x=\frac{0}{-4}$$

Divide 0 by -4.

$$x=0$$

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

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

Divide -4 by -4.

$$x=1$$

The equation is now solved.

$$x=0 x=1$$

Steps for Completing the Square

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

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

Divide both sides by -2.

$$\frac{-2x^{2}+2x}{-2}=\frac{0}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{2}{-2}x=\frac{0}{-2}$$

Divide 2 by -2.

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

Divide 0 by -2.

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

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

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

Factor x^{2}-x+\frac{1}{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}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

Add \frac{1}{2} to both sides of the equation.

$$x=1 x=0$$