Solve 20^2cm=x^2+10^2

$$20 ^ { 2 } cm = x ^ { 2 } + 10 ^ { 2 }$$

Solve for c (complex solution)

$$\left\{\begin{matrix}c=\frac{x^{2}+100}{400m}\text{, }&m\neq 0\\c\in \mathrm{C}\text{, }&\left(x=-10i\text{ or }x=10i\right)\text{ and }m=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 20 to the power of 2 and get 400.

$$400cm=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$400cm=x^{2}+100$$

The equation is in standard form.

$$400mc=x^{2}+100$$

Divide both sides by 400m.

$$\frac{400mc}{400m}=\frac{x^{2}+100}{400m}$$

Dividing by 400m undoes the multiplication by 400m.

$$c=\frac{x^{2}+100}{400m}$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{x^{2}+100}{400c}\text{, }&c\neq 0\\m\in \mathrm{C}\text{, }&\left(x=-10i\text{ or }x=10i\right)\text{ and }c=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 20 to the power of 2 and get 400.

$$400cm=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$400cm=x^{2}+100$$

Divide both sides by 400c.

$$\frac{400cm}{400c}=\frac{x^{2}+100}{400c}$$

Dividing by 400c undoes the multiplication by 400c.

$$m=\frac{x^{2}+100}{400c}$$

Solve for c

$$c=\frac{x^{2}+100}{400m}$$

$$m\neq 0$$

Steps for Solving Linear Equation

Calculate 20 to the power of 2 and get 400.

$$400cm=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$400cm=x^{2}+100$$

The equation is in standard form.

$$400mc=x^{2}+100$$

Divide both sides by 400m.

$$\frac{400mc}{400m}=\frac{x^{2}+100}{400m}$$

Dividing by 400m undoes the multiplication by 400m.

$$c=\frac{x^{2}+100}{400m}$$

Solve for m

$$m=\frac{x^{2}+100}{400c}$$

$$c\neq 0$$

Steps for Solving Linear Equation

Calculate 20 to the power of 2 and get 400.

$$400cm=x^{2}+10^{2}$$

Calculate 10 to the power of 2 and get 100.

$$400cm=x^{2}+100$$

Divide both sides by 400c.

$$\frac{400cm}{400c}=\frac{x^{2}+100}{400c}$$

Dividing by 400c undoes the multiplication by 400c.

$$m=\frac{x^{2}+100}{400c}$$