Solve PV=nRTsqrt{x^2}

$$PV = nRT \sqrt{ { x }^{ 2 } }$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{RTn\sqrt{x^{2}}}{V}\text{, }&V\neq 0\\P\in \mathrm{C}\text{, }&\left(n=0\text{ or }R=0\text{ or }T=0\text{ or }x=0\right)\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$VP=RTn\sqrt{x^{2}}$$

Divide both sides by V.

$$\frac{VP}{V}=\frac{RTn\sqrt{x^{2}}}{V}$$

Dividing by V undoes the multiplication by V.

$$P=\frac{RTn\sqrt{x^{2}}}{V}$$

Solve for R (complex solution)

$$\left\{\begin{matrix}R=\frac{\left(x^{2}\right)^{-\frac{1}{2}}PV}{Tn}\text{, }&x\neq 0\text{ and }T\neq 0\text{ and }n\neq 0\\R\in \mathrm{C}\text{, }&\left(P=0\text{ and }T=0\right)\text{ or }\left(P=0\text{ and }x=0\right)\text{ or }\left(T=0\text{ and }V=0\right)\text{ or }\left(x=0\text{ and }V=0\right)\text{ or }\left(V=0\text{ and }n=0\text{ and }x\neq 0\text{ and }T\neq 0\right)\text{ or }\left(P=0\text{ and }n=0\text{ and }x\neq 0\text{ and }T\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nRT\sqrt{x^{2}}=PV$$

The equation is in standard form.

$$Tn\sqrt{x^{2}}R=PV$$

Divide both sides by nT\sqrt{x^{2}}.

$$\frac{Tn\sqrt{x^{2}}R}{Tn\sqrt{x^{2}}}=\frac{PV}{Tn\sqrt{x^{2}}}$$

Dividing by nT\sqrt{x^{2}} undoes the multiplication by nT\sqrt{x^{2}}.

$$R=\frac{PV}{Tn\sqrt{x^{2}}}$$

Divide PV by nT\sqrt{x^{2}}.

$$R=\frac{\left(x^{2}\right)^{-\frac{1}{2}}PV}{Tn}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{RTn|x|}{V}\text{, }&V\neq 0\\P\in \mathrm{R}\text{, }&\left(n=0\text{ or }R=0\text{ or }T=0\text{ or }x=0\right)\text{ and }V=0\end{matrix}\right.$$

Steps for Solving Linear Equation

The equation is in standard form.

$$VP=RTn\sqrt{x^{2}}$$

Divide both sides by V.

$$\frac{VP}{V}=\frac{RTn|x|}{V}$$

Dividing by V undoes the multiplication by V.

$$P=\frac{RTn|x|}{V}$$

Solve for R

$$\left\{\begin{matrix}R=\frac{PV}{Tn|x|}\text{, }&n\neq 0\text{ and }T\neq 0\text{ and }x\neq 0\\R\in \mathrm{R}\text{, }&\left(P=0\text{ and }T=0\right)\text{ or }\left(P=0\text{ and }x=0\right)\text{ or }\left(T=0\text{ and }V=0\right)\text{ or }\left(x=0\text{ and }V=0\right)\text{ or }\left(V=0\text{ and }n=0\text{ and }T\neq 0\text{ and }x\neq 0\right)\text{ or }\left(P=0\text{ and }n=0\text{ and }T\neq 0\text{ and }x\neq 0\right)\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$nRT\sqrt{x^{2}}=PV$$

The equation is in standard form.

$$Tn\sqrt{x^{2}}R=PV$$

Divide both sides by nT\sqrt{x^{2}}.

$$\frac{Tn\sqrt{x^{2}}R}{Tn\sqrt{x^{2}}}=\frac{PV}{Tn\sqrt{x^{2}}}$$

Dividing by nT\sqrt{x^{2}} undoes the multiplication by nT\sqrt{x^{2}}.

$$R=\frac{PV}{Tn\sqrt{x^{2}}}$$

Divide PV by nT\sqrt{x^{2}}.

$$R=\frac{PV}{Tn|x|}$$