To form a perfect-square trinomial from the expression [tex]\(x^2 - 5x\)[/tex], we need to add a specific term. A perfect-square trinomial is an expression that can be written in the form [tex]\((x + a)^2\)[/tex] or [tex]\((x - a)^2\)[/tex]. In our case, we are starting with the expression [tex]\(x^2 - 5x\)[/tex].
Here are the steps to complete the square:
1. Identify the coefficient of [tex]\(x\)[/tex], which is [tex]\(-5\)[/tex].
2. Take half of this coefficient. So, [tex]\(-5 / 2 = -2.5\)[/tex].
3. Square this result to complete the square. So, [tex]\((-2.5)^2 = 6.25\)[/tex].
Hence, the expression [tex]\(x^2 - 5x\)[/tex] needs the term [tex]\(6.25\)[/tex] to be added to become a perfect-square trinomial.
Thus, the completed perfect-square trinomial is:
[tex]\[
x^2 - 5x + 6.25
\][/tex]
In conclusion, the value added to complete the square for the expression [tex]\(x^2 - 5x\)[/tex] is:
[tex]\[
\boxed{6.25}
\][/tex]
