Solve 1/4m^2-1/2m-2-1/2m+2=0

$$\frac { 1 } { 4 } m ^ { 2 } - \frac { 1 } { 2 } m - 2 - \frac { 1 } { 2 } m + 2 = 0$$

Solve for m

$$m=4$$

$$m=0$$

Steps Using Factoring

Combine -\frac{1}{2}m and -\frac{1}{2}m to get -m.

$$\frac{1}{4}m^{2}-m-2+2=0$$

Add -2 and 2 to get 0.

$$\frac{1}{4}m^{2}-m=0$$

Factor out m.

$$m\left(\frac{1}{4}m-1\right)=0$$

To find equation solutions, solve m=0 and \frac{m}{4}-1=0.

$$m=0 m=4$$

Steps Using the Quadratic Formula

Combine -\frac{1}{2}m and -\frac{1}{2}m to get -m.

$$\frac{1}{4}m^{2}-m-2+2=0$$

Add -2 and 2 to get 0.

$$\frac{1}{4}m^{2}-m=0$$

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

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

Take the square root of 1.

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

The opposite of -1 is 1.

$$m=\frac{1±1}{2\times \frac{1}{4}}$$

Multiply 2 times \frac{1}{4}.

$$m=\frac{1±1}{\frac{1}{2}}$$

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

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

Divide 2 by \frac{1}{2} by multiplying 2 by the reciprocal of \frac{1}{2}.

$$m=4$$

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

$$m=\frac{0}{\frac{1}{2}}$$

Divide 0 by \frac{1}{2} by multiplying 0 by the reciprocal of \frac{1}{2}.

$$m=0$$

The equation is now solved.

$$m=4 m=0$$

Steps for Completing the Square

Combine -\frac{1}{2}m and -\frac{1}{2}m to get -m.

$$\frac{1}{4}m^{2}-m-2+2=0$$

Add -2 and 2 to get 0.

$$\frac{1}{4}m^{2}-m=0$$

Multiply both sides by 4.

$$\frac{\frac{1}{4}m^{2}-m}{\frac{1}{4}}=\frac{0}{\frac{1}{4}}$$

Dividing by \frac{1}{4} undoes the multiplication by \frac{1}{4}.

$$m^{2}+\left(-\frac{1}{\frac{1}{4}}\right)m=\frac{0}{\frac{1}{4}}$$

Divide -1 by \frac{1}{4} by multiplying -1 by the reciprocal of \frac{1}{4}.

$$m^{2}-4m=\frac{0}{\frac{1}{4}}$$

Divide 0 by \frac{1}{4} by multiplying 0 by the reciprocal of \frac{1}{4}.

$$m^{2}-4m=0$$

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

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

Square -2.

$$m^{2}-4m+4=4$$

Factor m^{2}-4m+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}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$m-2=2 m-2=-2$$

Add 2 to both sides of the equation.

$$m=4 m=0$$