Solve Pr=(x-a)^2

$$P r = ( x - a ) ^ { 2 }$$

Solve for P (complex solution)

$$\left\{\begin{matrix}P=\frac{\left(x-a\right)^{2}}{r}\text{, }&r\neq 0\\P\in \mathrm{C}\text{, }&x=a\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(x-a\right)^{2}.

$$Pr=x^{2}-2xa+a^{2}$$

The equation is in standard form.

$$rP=x^{2}-2ax+a^{2}$$

Divide both sides by r.

$$\frac{rP}{r}=\frac{\left(x-a\right)^{2}}{r}$$

Dividing by r undoes the multiplication by r.

$$P=\frac{\left(x-a\right)^{2}}{r}$$

Solve for P

$$\left\{\begin{matrix}P=\frac{\left(x-a\right)^{2}}{r}\text{, }&r\neq 0\\P\in \mathrm{R}\text{, }&x=a\text{ and }r=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(x-a\right)^{2}.

$$Pr=x^{2}-2xa+a^{2}$$

The equation is in standard form.

$$rP=x^{2}-2ax+a^{2}$$

Divide both sides by r.

$$\frac{rP}{r}=\frac{\left(x-a\right)^{2}}{r}$$

Dividing by r undoes the multiplication by r.

$$P=\frac{\left(x-a\right)^{2}}{r}$$

Solve for a (complex solution)

$$a=\sqrt{P}\sqrt{r}+x$$

$$a=-\sqrt{P}\sqrt{r}+x$$

Solve for a

$$a=\sqrt{Pr}+x$$

$$a=-\sqrt{Pr}+x\text{, }\left(r\geq 0\text{ and }P\geq 0\right)\text{ or }\left(P\leq 0\text{ and }r\leq 0\right)$$