Solve m+2=3/m

$$m + 2 = \frac { 3 } { m }$$

Solve for m

$$m=-3$$

$$m=1$$

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 m.

$$mm+m\times 2=3$$

Multiply m and m to get m^{2}.

$$m^{2}+m\times 2=3$$

Subtract 3 from both sides.

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

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.

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

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}.

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

Square 2.

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

Multiply -4 times -3.

$$m=\frac{-2±\sqrt{4+12}}{2}$$

Add 4 to 12.

$$m=\frac{-2±\sqrt{16}}{2}$$

Take the square root of 16.

$$m=\frac{-2±4}{2}$$

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 m.

$$mm+m\times 2=3$$

Multiply m and m to get m^{2}.

$$m^{2}+m\times 2=3$$

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.

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

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.

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

Square 1.

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

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.

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

Subtract 1 from both sides of the equation.

$$m=1 m=-3$$