Solve =(300m/5)^2/3*108frac{m{3}}=1

$$= \frac { ( 300 \frac { m } { 5 } ) ^ { 2 } } { 3 \cdot 108 \frac { m } { 3 } } = 1$$

Solve for m

$$m=\frac{3}{100}=0.03$$

Steps Using Factoring

Cancel out 5, the greatest common factor in 300 and 5.

$$\frac{\left(60m\right)^{2}}{3\times 108\times \frac{m}{3}}=1$$

Expand \left(60m\right)^{2}.

$$\frac{60^{2}m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{3600m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Multiply 3 and 108 to get 324.

$$\frac{3600m^{2}}{324\times \frac{m}{3}}=1$$

Cancel out 3, the greatest common factor in 324 and 3.

$$\frac{3600m^{2}}{108m}=1$$

Cancel out 36 in both numerator and denominator.

$$\frac{100m^{2}}{3m}=1$$

Subtract 1 from both sides.

$$\frac{100m^{2}}{3m}-1=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3m}{3m}.

$$\frac{100m^{2}}{3m}-\frac{3m}{3m}=0$$

Since \frac{100m^{2}}{3m} and \frac{3m}{3m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100m^{2}-3m}{3m}=0$$

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

$$100m^{2}-3m=0$$

Factor out m.

$$m\left(100m-3\right)=0$$

To find equation solutions, solve m=0 and 100m-3=0.

$$m=0 m=\frac{3}{100}$$

Variable m cannot be equal to 0.

$$m=\frac{3}{100}$$

Steps Using the Quadratic Formula

Cancel out 5, the greatest common factor in 300 and 5.

$$\frac{\left(60m\right)^{2}}{3\times 108\times \frac{m}{3}}=1$$

Expand \left(60m\right)^{2}.

$$\frac{60^{2}m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{3600m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Multiply 3 and 108 to get 324.

$$\frac{3600m^{2}}{324\times \frac{m}{3}}=1$$

Cancel out 3, the greatest common factor in 324 and 3.

$$\frac{3600m^{2}}{108m}=1$$

Cancel out 36 in both numerator and denominator.

$$\frac{100m^{2}}{3m}=1$$

Subtract 1 from both sides.

$$\frac{100m^{2}}{3m}-1=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 1 times \frac{3m}{3m}.

$$\frac{100m^{2}}{3m}-\frac{3m}{3m}=0$$

Since \frac{100m^{2}}{3m} and \frac{3m}{3m} have the same denominator, subtract them by subtracting their numerators.

$$\frac{100m^{2}-3m}{3m}=0$$

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

$$100m^{2}-3m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, -3 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}}}{2\times 100}$$

Take the square root of \left(-3\right)^{2}.

$$m=\frac{-\left(-3\right)±3}{2\times 100}$$

The opposite of -3 is 3.

$$m=\frac{3±3}{2\times 100}$$

Multiply 2 times 100.

$$m=\frac{3±3}{200}$$

Now solve the equation m=\frac{3±3}{200} when ± is plus. Add 3 to 3.

$$m=\frac{6}{200}$$

Reduce the fraction \frac{6}{200} to lowest terms by extracting and canceling out 2.

$$m=\frac{3}{100}$$

Now solve the equation m=\frac{3±3}{200} when ± is minus. Subtract 3 from 3.

$$m=\frac{0}{200}$$

Divide 0 by 200.

$$m=0$$

The equation is now solved.

$$m=\frac{3}{100} m=0$$

Variable m cannot be equal to 0.

$$m=\frac{3}{100}$$

Steps for Completing the Square

Cancel out 5, the greatest common factor in 300 and 5.

$$\frac{\left(60m\right)^{2}}{3\times 108\times \frac{m}{3}}=1$$

Expand \left(60m\right)^{2}.

$$\frac{60^{2}m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Calculate 60 to the power of 2 and get 3600.

$$\frac{3600m^{2}}{3\times 108\times \frac{m}{3}}=1$$

Multiply 3 and 108 to get 324.

$$\frac{3600m^{2}}{324\times \frac{m}{3}}=1$$

Cancel out 3, the greatest common factor in 324 and 3.

$$\frac{3600m^{2}}{108m}=1$$

Cancel out 36 in both numerator and denominator.

$$\frac{100m^{2}}{3m}=1$$

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

$$100m^{2}=3m$$

Subtract 3m from both sides.

$$100m^{2}-3m=0$$

Divide both sides by 100.

$$\frac{100m^{2}-3m}{100}=\frac{0}{100}$$

Dividing by 100 undoes the multiplication by 100.

$$m^{2}-\frac{3}{100}m=\frac{0}{100}$$

Divide 0 by 100.

$$m^{2}-\frac{3}{100}m=0$$

Divide -\frac{3}{100}, the coefficient of the x term, by 2 to get -\frac{3}{200}. Then add the square of -\frac{3}{200} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{3}{100}m+\left(-\frac{3}{200}\right)^{2}=\left(-\frac{3}{200}\right)^{2}$$

Square -\frac{3}{200} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{3}{100}m+\frac{9}{40000}=\frac{9}{40000}$$

Factor m^{2}-\frac{3}{100}m+\frac{9}{40000}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{3}{200}\right)^{2}=\frac{9}{40000}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{3}{200}\right)^{2}}=\sqrt{\frac{9}{40000}}$$

Simplify.

$$m-\frac{3}{200}=\frac{3}{200} m-\frac{3}{200}=-\frac{3}{200}$$

Add \frac{3}{200} to both sides of the equation.

$$m=\frac{3}{100} m=0$$

Variable m cannot be equal to 0.

$$m=\frac{3}{100}$$