Solve e=c/a*frac{sqrt{2}}{2}

$$e = \frac { c } { a } \cdot \frac { \sqrt { 2 } } { 2 }$$

Solve for a

$$a=\frac{\sqrt{2}c}{2e}$$

$$c\neq 0$$

Steps for Solving Linear Equation

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$e\times 2a=2c\times \frac{\sqrt{2}}{2}$$

Express 2\times \frac{\sqrt{2}}{2} as a single fraction.

$$e\times 2a=\frac{2\sqrt{2}}{2}c$$

Cancel out 2 and 2.

$$e\times 2a=\sqrt{2}c$$

The equation is in standard form.

$$2ea=\sqrt{2}c$$

Divide both sides by 2e.

$$\frac{2ea}{2e}=\frac{\sqrt{2}c}{2e}$$

Dividing by 2e undoes the multiplication by 2e.

$$a=\frac{\sqrt{2}c}{2e}$$

Variable a cannot be equal to 0.

$$a=\frac{\sqrt{2}c}{2e}\text{, }a\neq 0$$

Solve for c

$$c=e\sqrt{2}a$$

$$a\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2a, the least common multiple of a,2.

$$e\times 2a=2c\times \frac{\sqrt{2}}{2}$$

Express 2\times \frac{\sqrt{2}}{2} as a single fraction.

$$e\times 2a=\frac{2\sqrt{2}}{2}c$$

Cancel out 2 and 2.

$$e\times 2a=\sqrt{2}c$$

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

$$\sqrt{2}c=e\times 2a$$

The equation is in standard form.

$$\sqrt{2}c=2ea$$

Divide both sides by \sqrt{2}.

$$\frac{\sqrt{2}c}{\sqrt{2}}=\frac{2ea}{\sqrt{2}}$$

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

$$c=\frac{2ea}{\sqrt{2}}$$

Divide 2ea by \sqrt{2}.

$$c=e\sqrt{2}a$$