Complete the square. Write the resulting perfect-square trinomial as the square of a binomial. $$ x^{2}-10 x+\square=(\square) $$

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To complete the square, we need to add a term that will make the expression a perfect square trinomial. The general form of a perfect square trinomial is $$ (x - a)^2 = x^2 - 2ax + a^2 $$.

In the given expression $$ x^2 - 10x + \square $$, we can see that the middle term is $$ -10x $$, which corresponds to $$ -2ax $$ in the general form. To find $$ a $$, we divide the coefficient of $$ x $$ by 2:

$$ a = \frac{-10}{2} = -5 $$

Now we know that $$ a^2 = (-5)^2 = 25 $$. This is the term we need to add to the expression to complete the square.

So, the completed square is:

$$ x^2 - 10x + 25 $$

And this can be written as the square of a binomial:

$$ (x - 5)^2 $$

Therefore, the completed square is:

$$ x^2 - 10x + 25 = (x - 5)^2 $$
$$ x^2 - 10x + 25 = (x - 5)^2 $$

Complete the square. Write the resulting perfect-square trinomial as the square of a binomial. \( x^{2}-10 x+\square=(\square) \)

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