Solve -m/1=3/4+m

$$\frac { - m } { 1 } = \frac { 3 } { 4 + m }$$

Solve for m

$$m=-3$$

$$m=-1$$

Steps Using the Quadratic Formula

Variable m cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by m+4.

$$\left(m+4\right)\left(-m\right)=3$$

Use the distributive property to multiply m+4 by -m.

$$m\left(-m\right)+4\left(-m\right)=3$$

Subtract 3 from both sides.

$$m\left(-m\right)+4\left(-m\right)-3=0$$

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

$$m^{2}\left(-1\right)+4\left(-1\right)m-3=0$$

Multiply 4 and -1 to get -4.

$$m^{2}\left(-1\right)-4m-3=0$$

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.

$$-m^{2}-4m-3=0$$

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

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

Square -4.

$$m=\frac{-\left(-4\right)±\sqrt{16-4\left(-1\right)\left(-3\right)}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$m=\frac{-\left(-4\right)±\sqrt{16+4\left(-3\right)}}{2\left(-1\right)}$$

Multiply 4 times -3.

$$m=\frac{-\left(-4\right)±\sqrt{16-12}}{2\left(-1\right)}$$

Add 16 to -12.

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

Take the square root of 4.

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

The opposite of -4 is 4.

$$m=\frac{4±2}{2\left(-1\right)}$$

Multiply 2 times -1.

$$m=\frac{4±2}{-2}$$

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

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

Divide 6 by -2.

$$m=-3$$

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

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

Divide 2 by -2.

$$m=-1$$

The equation is now solved.

$$m=-3 m=-1$$

Steps for Completing the Square

Variable m cannot be equal to -4 since division by zero is not defined. Multiply both sides of the equation by m+4.

$$\left(m+4\right)\left(-m\right)=3$$

Use the distributive property to multiply m+4 by -m.

$$m\left(-m\right)+4\left(-m\right)=3$$

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

$$m^{2}\left(-1\right)+4\left(-1\right)m=3$$

Multiply 4 and -1 to get -4.

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

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.

$$-m^{2}-4m=3$$

Divide both sides by -1.

$$\frac{-m^{2}-4m}{-1}=\frac{3}{-1}$$

Dividing by -1 undoes the multiplication by -1.

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

Divide -4 by -1.

$$m^{2}+4m=\frac{3}{-1}$$

Divide 3 by -1.

$$m^{2}+4m=-3$$

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

$$m^{2}+4m+2^{2}=-3+2^{2}$$

Square 2.

$$m^{2}+4m+4=-3+4$$

Add -3 to 4.

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

Factor m^{2}+4m+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}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

Subtract 2 from both sides of the equation.

$$m=-1 m=-3$$