Solve m+1=14-m/2m

$$m + 1 = \frac { 14 - m } { 2 m }$$

Solve for m

$$m = -\frac{7}{2} = -3\frac{1}{2} = -3.5$$

$$m=2$$

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 2m.

$$2mm+2m=14-m$$

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

$$2m^{2}+2m=14-m$$

Subtract 14 from both sides.

$$2m^{2}+2m-14=-m$$

Add m to both sides.

$$2m^{2}+2m-14+m=0$$

Combine 2m and m to get 3m.

$$2m^{2}+3m-14=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 3 for b, and -14 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-3±\sqrt{3^{2}-4\times 2\left(-14\right)}}{2\times 2}$$

Square 3.

$$m=\frac{-3±\sqrt{9-4\times 2\left(-14\right)}}{2\times 2}$$

Multiply -4 times 2.

$$m=\frac{-3±\sqrt{9-8\left(-14\right)}}{2\times 2}$$

Multiply -8 times -14.

$$m=\frac{-3±\sqrt{9+112}}{2\times 2}$$

Add 9 to 112.

$$m=\frac{-3±\sqrt{121}}{2\times 2}$$

Take the square root of 121.

$$m=\frac{-3±11}{2\times 2}$$

Multiply 2 times 2.

$$m=\frac{-3±11}{4}$$

Now solve the equation m=\frac{-3±11}{4} when ± is plus. Add -3 to 11.

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

Divide 8 by 4.

$$m=2$$

Now solve the equation m=\frac{-3±11}{4} when ± is minus. Subtract 11 from -3.

$$m=-\frac{14}{4}$$

Reduce the fraction \frac{-14}{4} to lowest terms by extracting and canceling out 2.

$$m=-\frac{7}{2}$$

The equation is now solved.

$$m=2 m=-\frac{7}{2}$$

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 2m.

$$2mm+2m=14-m$$

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

$$2m^{2}+2m=14-m$$

Add m to both sides.

$$2m^{2}+2m+m=14$$

Combine 2m and m to get 3m.

$$2m^{2}+3m=14$$

Divide both sides by 2.

$$\frac{2m^{2}+3m}{2}=\frac{14}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$m^{2}+\frac{3}{2}m=\frac{14}{2}$$

Divide 14 by 2.

$$m^{2}+\frac{3}{2}m=7$$

Divide \frac{3}{2}, the coefficient of the x term, by 2 to get \frac{3}{4}. Then add the square of \frac{3}{4} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}+\frac{3}{2}m+\left(\frac{3}{4}\right)^{2}=7+\left(\frac{3}{4}\right)^{2}$$

Square \frac{3}{4} by squaring both the numerator and the denominator of the fraction.

$$m^{2}+\frac{3}{2}m+\frac{9}{16}=7+\frac{9}{16}$$

Add 7 to \frac{9}{16}.

$$m^{2}+\frac{3}{2}m+\frac{9}{16}=\frac{121}{16}$$

Factor m^{2}+\frac{3}{2}m+\frac{9}{16}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m+\frac{3}{4}\right)^{2}=\frac{121}{16}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m+\frac{3}{4}\right)^{2}}=\sqrt{\frac{121}{16}}$$

Simplify.

$$m+\frac{3}{4}=\frac{11}{4} m+\frac{3}{4}=-\frac{11}{4}$$

Subtract \frac{3}{4} from both sides of the equation.

$$m=2 m=-\frac{7}{2}$$