Solve m^2/3m=1

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

Solve for m

$$m=3$$

Steps Using Factoring

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

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

Subtract 3m from both sides.

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

Factor out m.

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

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

$$m=0 m=3$$

Variable m cannot be equal to 0.

$$m=3$$

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 3m.

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

Subtract 3m from both sides.

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

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

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

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

$$m=\frac{-\left(-3\right)±3}{2}$$

The opposite of -3 is 3.

$$m=\frac{3±3}{2}$$

Now solve the equation m=\frac{3±3}{2} when ± is plus. Add 3 to 3.

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

Divide 6 by 2.

$$m=3$$

Now solve the equation m=\frac{3±3}{2} when ± is minus. Subtract 3 from 3.

$$m=\frac{0}{2}$$

Divide 0 by 2.

$$m=0$$

The equation is now solved.

$$m=3 m=0$$

Variable m cannot be equal to 0.

$$m=3$$

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 3m.

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

Subtract 3m from both sides.

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

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

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

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$m^{2}-3m+\frac{9}{4}=\frac{9}{4}$$

Factor m^{2}-3m+\frac{9}{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}.

$$\left(m-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

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

Simplify.

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

Add \frac{3}{2} to both sides of the equation.

$$m=3 m=0$$

Variable m cannot be equal to 0.

$$m=3$$