To transform the quadratic expression [tex]\( x^2 - 10x + \square \)[/tex] into a perfect square trinomial, we need to follow these steps:
1. Identify the coefficient of the linear term: The linear term in the expression is [tex]\( -10x \)[/tex]. Therefore, the coefficient of [tex]\( x \)[/tex] is [tex]\(-10\)[/tex].
2. Find half of this coefficient: Divide [tex]\(-10\)[/tex] by 2 to get [tex]\(-5\)[/tex].
3. Square the result from step 2: Now, square [tex]\(-5\)[/tex] to get [tex]\((-5)^2 = 25\)[/tex].
So, the value that completes the perfect square trinomial is 25.
Thus, the completed perfect square trinomial is:
[tex]\[ x^2 - 10x + 25 \][/tex]
