To complete the square for the equation \(x^{2} - 2x + 1 = 0\), we can follow these steps:
- Start with the expression \(x^2 - 2x + 1\).
- Notice that the expression can be rewritten as a perfect square. Specifically, we can see that: \[ x^2 - 2x + 1 = (x - 1)^2 \]
- 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 \(0\).
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