Solve the Equation: (x-1)² = x² | Comparing Perfect Squares

Let's examine the given equation:

$(x-1)^2=x^2$First, let's simplify the equation, using the perfect square binomial formula:

$(a\pm b)^2=a^2\pm2ab+b^2$,

We'll start by opening the parentheses on the left side using the perfect square formula and then move terms and combine like terms, in the final step we'll solve the resulting simplified equation:

$(x-1)^2=x^2 \\ \downarrow\\ x^2-2\cdot x\cdot1+1^2=x^2\\ x^2-2x+1= x^2\\ -2x=-1\hspace{6pt}\text{/}:(-2)\\ \boxed{x=\frac{1}{2}}$Therefore, the correct answer is answer A.