To find the missing coefficient of the [tex]$x$[/tex]-term in the expression [tex]$(-x-5)^2$[/tex] after it has been simplified, we need to follow these steps:
1. Start with the given expression:
[tex]\[
(-x-5)^2
\][/tex]
2. Expand the expression using the distributive property (also known as the FOIL method for binomials):
[tex]\[
(-x-5) \cdot (-x-5)
\][/tex]
3. Apply the distributive property:
[tex]\[
(-x-5)(-x-5) = (-x)(-x) + (-x)(-5) + (-5)(-x) + (-5)(-5)
\][/tex]
4. Multiply the terms inside the parenthesis:
[tex]\[
(-x)(-x) = x^2
\][/tex]
[tex]\[
(-x)(-5) = 5x
\][/tex]
[tex]\[
(-5)(-x) = 5x
\][/tex]
[tex]\[
(-5)(-5) = 25
\][/tex]
5. Combine like terms to simplify the expression:
[tex]\[
x^2 + 5x + 5x + 25
\][/tex]
6. Add the like terms:
[tex]\[
x^2 + 10x + 25
\][/tex]
The simplified expression is:
[tex]\[
x^2 + 10x + 25
\][/tex]
From this simplified expression, we can see that the coefficient of the [tex]$x$[/tex]-term is [tex]\(10\)[/tex].
Therefore, the missing coefficient of the [tex]$x$[/tex]-term is [tex]\(10\)[/tex].
The correct answer is:
[tex]\[
\boxed{10}
\][/tex]
