Complete the square for \[ x^{2}-12 x+\ldots-- \]

To complete the square for the expression \( x^{2}-12x+\ldots \), we start by focusing on the quadratic part. First, take the coefficient of \( x \), which is \(-12\), divide it by 2 to get \(-6\), and then square it to find \( (-6)^2 = 36 \). Next, we can rewrite the expression as: \[ x^{2}-12x + 36 - 36 \] This can then be presented in completed square form as: \[ (x - 6)^2 - 36 \] Now, if you have a specific number you want to add to the expression, you can adjust accordingly! Just remember that completing the square involves making a perfect square trinomial. Be cautious with signs when rearranging! It's easy to accidentally flip a sign, especially when moving terms around. Always double-check your calculations.