Solve O(x-3)^2=(2x-1)^2

$$O ( x - 3 ) ^ { 2 } = ( 2 x - 1 ) ^ { 2 }$$

Solve for O

$$O=\left(\frac{2x-1}{x-3}\right)^{2}$$

$$x\neq 3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-3\right)^{2}.

$$O\left(x^{2}-6x+9\right)=\left(2x-1\right)^{2}$$

Use the distributive property to multiply O by x^{2}-6x+9.

$$Ox^{2}-6Ox+9O=\left(2x-1\right)^{2}$$

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

$$Ox^{2}-6Ox+9O=4x^{2}-4x+1$$

Combine all terms containing O.

$$\left(x^{2}-6x+9\right)O=4x^{2}-4x+1$$

Divide both sides by x^{2}-6x+9.

$$\frac{\left(x^{2}-6x+9\right)O}{x^{2}-6x+9}=\frac{\left(2x-1\right)^{2}}{x^{2}-6x+9}$$

Dividing by x^{2}-6x+9 undoes the multiplication by x^{2}-6x+9.

$$O=\frac{\left(2x-1\right)^{2}}{x^{2}-6x+9}$$

Divide \left(2x-1\right)^{2} by x^{2}-6x+9.

$$O=\frac{\left(2x-1\right)^{2}}{\left(x-3\right)^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{3\sqrt{O}-1}{\sqrt{O}-2}\text{; }x=\frac{3\sqrt{O}+1}{\sqrt{O}+2}\text{, }&O\neq 4\\x=\frac{7}{4}\text{, }&O=4\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{3\sqrt{O}-1}{\sqrt{O}-2}\text{; }x=\frac{3\sqrt{O}+1}{\sqrt{O}+2}\text{, }&O\neq 4\text{ and }O\geq 0\\x=\frac{7}{4}\text{, }&O=4\end{matrix}\right.$$