Question

Rewrite the equation by completing the square.
\[x^{2}-2x+1 = 0\]
\[(x + {}\]

\[)^2 = {}\]

Answer 1

To complete the square for the equation \(x^{2} - 2x + 1 = 0\), we can follow these steps:

1. Start with the expression \(x^2 - 2x + 1\).
2. Notice that the expression can be rewritten as a perfect square. Specifically, we can see that:
\[
x^2 - 2x + 1 = (x - 1)^2
\]
3. Therefore, the equation \(x^{2} - 2x + 1 = 0\) can be written as:
\[
(x - 1)^2 = 0
\]

Putting this into the format you requested:

\[
(x + \text{ })^2 = \text{ }
\]

This gives:

\[
(x - 1)^2 = 0
\]

So, we have completed the square as follows:

\[
(x - 1)^2 = 0
\]

Thus, the final rewritten form is:

\[
(x + (-1))^2 = 0
\]

So, to explicitly answer your format:

\[
(x + (-1))^2 = 0
\]

Here, the blank for \(x + \text{ }\) is \(-1\) and the blank for the other side is \(0\).