Solve -2/2-2m=1-m/-1

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

Solve for m

$$m=2$$

$$m=0$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(m-1\right), the least common multiple of 2-2m,-1.

$$-\left(-2\right)=\left(-2m+2\right)\left(1-m\right)$$

Multiply -1 and -2 to get 2.

$$2=\left(-2m+2\right)\left(1-m\right)$$

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

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

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

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

Take the square root of \left(-4\right)^{2}.

$$m=\frac{-\left(-4\right)±4}{2\times 2}$$

The opposite of -4 is 4.

$$m=\frac{4±4}{2\times 2}$$

Multiply 2 times 2.

$$m=\frac{4±4}{4}$$

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

$$m=\frac{8}{4}$$

Divide 8 by 4.

$$m=2$$

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

$$m=\frac{0}{4}$$

Divide 0 by 4.

$$m=0$$

The equation is now solved.

$$m=2 m=0$$

Steps for Completing the Square

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(m-1\right), the least common multiple of 2-2m,-1.

$$-\left(-2\right)=\left(-2m+2\right)\left(1-m\right)$$

Multiply -1 and -2 to get 2.

$$2=\left(-2m+2\right)\left(1-m\right)$$

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

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

Swap sides so that all variable terms are on the left hand side.

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

Subtract 2 from both sides.

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

Subtract 2 from 2 to get 0.

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

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

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

Divide both sides by 2.

$$\frac{2m^{2}-4m}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m^{2}+\left(-\frac{4}{2}\right)m=\frac{0}{2}$$

Divide -4 by 2.

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

Divide 0 by 2.

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

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

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

Factor m^{2}-2m+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

$$\sqrt{\left(m-1\right)^{2}}=\sqrt{1}$$

Simplify.

$$m-1=1 m-1=-1$$

Add 1 to both sides of the equation.

$$m=2 m=0$$