Solve x+n^2x=36200

$$x + n ^ { 2 } x = 36200$$

Solve for x (complex solution)

$$x=\frac{36200}{n^{2}+1}$$

$$n\neq -i\text{ and }n\neq i$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(1+n^{2}\right)x=36200$$

The equation is in standard form.

$$\left(n^{2}+1\right)x=36200$$

Divide both sides by 1+n^{2}.

$$\frac{\left(n^{2}+1\right)x}{n^{2}+1}=\frac{36200}{n^{2}+1}$$

Dividing by 1+n^{2} undoes the multiplication by 1+n^{2}.

$$x=\frac{36200}{n^{2}+1}$$

Solve for x

$$x=\frac{36200}{n^{2}+1}$$

Steps for Solving Linear Equation

Combine all terms containing x.

$$\left(1+n^{2}\right)x=36200$$

The equation is in standard form.

$$\left(n^{2}+1\right)x=36200$$

Divide both sides by 1+n^{2}.

$$\frac{\left(n^{2}+1\right)x}{n^{2}+1}=\frac{36200}{n^{2}+1}$$

Dividing by 1+n^{2} undoes the multiplication by 1+n^{2}.

$$x=\frac{36200}{n^{2}+1}$$

Solve for n (complex solution)

$$n=-\sqrt{-1+\frac{36200}{x}}$$

$$n=\sqrt{-1+\frac{36200}{x}}\text{, }x\neq 0$$

Solve for n

$$n=\sqrt{-1+\frac{36200}{x}}$$

$$n=-\sqrt{-1+\frac{36200}{x}}\text{, }x>0\text{ and }x\leq 36200$$