Solve -2/2-2m=frac{sqrt{2}}{2}

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

Solve for m

$$m=\sqrt{2}+1\approx 2.414213562$$

Steps for Solving Linear Equation

Variable m cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by 2\left(m-1\right), the least common multiple of 2-2m,2.

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

Multiply -1 and -2 to get 2.

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

Use the distributive property to multiply m-1 by \sqrt{2}.

$$2=m\sqrt{2}-\sqrt{2}$$

Swap sides so that all variable terms are on the left hand side.

$$m\sqrt{2}-\sqrt{2}=2$$

Add \sqrt{2} to both sides.

$$m\sqrt{2}=2+\sqrt{2}$$

The equation is in standard form.

$$\sqrt{2}m=\sqrt{2}+2$$

Divide both sides by \sqrt{2}.

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

Dividing by \sqrt{2} undoes the multiplication by \sqrt{2}.

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

Divide 2+\sqrt{2} by \sqrt{2}.

$$m=\sqrt{2}+1$$