Solve 7mm=7m

$$7 m m = 7 m$$

Solve for m

$$m=1$$

$$m=0$$

Steps Using Factoring

Cancel out 7 on both sides.

$$mm=m$$

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

$$m^{2}=m$$

Subtract m from both sides.

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

Factor out m.

$$m\left(m-1\right)=0$$

To find equation solutions, solve m=0 and m-1=0.

$$m=0 m=1$$

Steps Using the Quadratic Formula

Cancel out 7 on both sides.

$$mm=m$$

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

$$m^{2}=m$$

Subtract m from both sides.

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

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

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

Take the square root of 1.

$$m=\frac{-\left(-1\right)±1}{2}$$

The opposite of -1 is 1.

$$m=\frac{1±1}{2}$$

Now solve the equation m=\frac{1±1}{2} when ± is plus. Add 1 to 1.

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

Divide 2 by 2.

$$m=1$$

Now solve the equation m=\frac{1±1}{2} when ± is minus. Subtract 1 from 1.

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

Divide 0 by 2.

$$m=0$$

The equation is now solved.

$$m=1 m=0$$

Steps for Completing the Square

Cancel out 7 on both sides.

$$mm=m$$

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

$$m^{2}=m$$

Subtract m from both sides.

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

Divide -1, the coefficient of the x term, by 2 to get -\frac{1}{2}. Then add the square of -\frac{1}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

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

Factor m^{2}-m+\frac{1}{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}.

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

Take the square root of both sides of the equation.

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

Simplify.

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

Add \frac{1}{2} to both sides of the equation.

$$m=1 m=0$$