Solve r*(x-1)^2=4

$$r \times ( x - 1 ) ^ { 2 } = 4$$

Solve for r

$$r=\frac{4}{\left(x-1\right)^{2}}$$

$$x\neq 1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$r\left(x^{2}-2x+1\right)=4$$

Use the distributive property to multiply r by x^{2}-2x+1.

$$rx^{2}-2rx+r=4$$

Combine all terms containing r.

$$\left(x^{2}-2x+1\right)r=4$$

Divide both sides by x^{2}-2x+1.

$$\frac{\left(x^{2}-2x+1\right)r}{x^{2}-2x+1}=\frac{4}{x^{2}-2x+1}$$

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

$$r=\frac{4}{x^{2}-2x+1}$$

Divide 4 by x^{2}-2x+1.

$$r=\frac{4}{\left(x-1\right)^{2}}$$

Solve for x (complex solution)

$$x=2r^{-\frac{1}{2}}+1$$

$$x=1-2r^{-\frac{1}{2}}\text{, }r\neq 0$$

Solve for x

$$x=1+\frac{2}{\sqrt{r}}$$

$$x=1-\frac{2}{\sqrt{r}}\text{, }r>0$$