Solve 10m^2=73m

$$10 m ^ { 2 } = 73 m$$

Solve for m

$$m = \frac{73}{10} = 7\frac{3}{10} = 7.3$$

$$m=0$$

Steps Using Factoring

Subtract 73m from both sides.

$$10m^{2}-73m=0$$

Factor out m.

$$m\left(10m-73\right)=0$$

To find equation solutions, solve m=0 and 10m-73=0.

$$m=0 m=\frac{73}{10}$$

Steps Using the Quadratic Formula

Subtract 73m from both sides.

$$10m^{2}-73m=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 10 for a, -73 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$m=\frac{-\left(-73\right)±\sqrt{\left(-73\right)^{2}}}{2\times 10}$$

Take the square root of \left(-73\right)^{2}.

$$m=\frac{-\left(-73\right)±73}{2\times 10}$$

The opposite of -73 is 73.

$$m=\frac{73±73}{2\times 10}$$

Multiply 2 times 10.

$$m=\frac{73±73}{20}$$

Now solve the equation m=\frac{73±73}{20} when ± is plus. Add 73 to 73.

$$m=\frac{146}{20}$$

Reduce the fraction \frac{146}{20} to lowest terms by extracting and canceling out 2.

$$m=\frac{73}{10}$$

Now solve the equation m=\frac{73±73}{20} when ± is minus. Subtract 73 from 73.

$$m=\frac{0}{20}$$

Divide 0 by 20.

$$m=0$$

The equation is now solved.

$$m=\frac{73}{10} m=0$$

Steps for Completing the Square

Subtract 73m from both sides.

$$10m^{2}-73m=0$$

Divide both sides by 10.

$$\frac{10m^{2}-73m}{10}=\frac{0}{10}$$

Dividing by 10 undoes the multiplication by 10.

$$m^{2}-\frac{73}{10}m=\frac{0}{10}$$

Divide 0 by 10.

$$m^{2}-\frac{73}{10}m=0$$

Divide -\frac{73}{10}, the coefficient of the x term, by 2 to get -\frac{73}{20}. Then add the square of -\frac{73}{20} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$m^{2}-\frac{73}{10}m+\left(-\frac{73}{20}\right)^{2}=\left(-\frac{73}{20}\right)^{2}$$

Square -\frac{73}{20} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-\frac{73}{10}m+\frac{5329}{400}=\frac{5329}{400}$$

Factor m^{2}-\frac{73}{10}m+\frac{5329}{400}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(m-\frac{73}{20}\right)^{2}=\frac{5329}{400}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(m-\frac{73}{20}\right)^{2}}=\sqrt{\frac{5329}{400}}$$

Simplify.

$$m-\frac{73}{20}=\frac{73}{20} m-\frac{73}{20}=-\frac{73}{20}$$

Add \frac{73}{20} to both sides of the equation.

$$m=\frac{73}{10} m=0$$