Complete the square to form a true equation.
\[
x^{2}-2 x+\ldots=(x-\ldots)^{2}
\]
Answer
\(\boxed{x^{2}-2 x+1=(x-1)^{2}}\) is the completed square form of the given equation.
Step 1 ：Given the equation \(x^{2}-2 x+\ldots=(x-\ldots)^{2}\), we need to complete the square.
Step 2 ：A perfect square trinomial is of the form \((x-a)^2 = x^2 - 2ax + a^2\). Comparing this with the given equation, we can see that \(a\) should be 1.
Step 3 ：So, we need to find a value that, when added to the left side of the equation, makes it a perfect square trinomial. This value is \(a^2 = 1^2 = 1\).
Step 4 ：Substituting the value of \(a\) into the equation, we get \(x^{2}-2 x+1=(x-1)^{2}\).
Step 5 ：\(\boxed{x^{2}-2 x+1=(x-1)^{2}}\) is the completed square form of the given equation.
