Solve -1/m=-m-2/3

$$- \frac{ 1 }{ m } = - \frac{ m-2 }{ 3 }$$

Solve for m

$$m=-1$$

$$m=3$$

Steps Using the Quadratic Formula

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3m, the least common multiple of m,3.

$$-3=-m\left(m-2\right)$$

Use the distributive property to multiply m by m-2.

$$-3=-\left(m^{2}-2m\right)$$

To find the opposite of m^{2}-2m, find the opposite of each term.

$$-3=-m^{2}-\left(-2m\right)$$

The opposite of -2m is 2m.

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

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

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

Add 3 to both sides.

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

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

$$m=\frac{-2±\sqrt{2^{2}-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Square 2.

$$m=\frac{-2±\sqrt{4-4\left(-1\right)\times 3}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$m=\frac{-2±\sqrt{4+4\times 3}}{2\left(-1\right)}$$

Multiply 4 times 3.

$$m=\frac{-2±\sqrt{4+12}}{2\left(-1\right)}$$

Add 4 to 12.

$$m=\frac{-2±\sqrt{16}}{2\left(-1\right)}$$

Take the square root of 16.

$$m=\frac{-2±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$m=\frac{-2±4}{-2}$$

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

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

Divide 2 by -2.

$$m=-1$$

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

$$m=-\frac{6}{-2}$$

Divide -6 by -2.

$$m=3$$

The equation is now solved.

$$m=-1 m=3$$

Steps for Completing the Square

Variable m cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 3m, the least common multiple of m,3.

$$-3=-m\left(m-2\right)$$

Use the distributive property to multiply m by m-2.

$$-3=-\left(m^{2}-2m\right)$$

To find the opposite of m^{2}-2m, find the opposite of each term.

$$-3=-m^{2}-\left(-2m\right)$$

The opposite of -2m is 2m.

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

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

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

Divide both sides by -1.

$$\frac{-m^{2}+2m}{-1}=-\frac{3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

$$m^{2}+\frac{2}{-1}m=-\frac{3}{-1}$$

Divide 2 by -1.

$$m^{2}-2m=-\frac{3}{-1}$$

Divide -3 by -1.

$$m^{2}-2m=3$$

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.

$$m^{2}-2m+1=3+1$$

Add 3 to 1.

$$m^{2}-2m+1=4$$

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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$m-1=2 m-1=-2$$

Add 1 to both sides of the equation.

$$m=3 m=-1$$