Let's solve for the value of the expression [tex]\( w^2 + 3w - 11 \)[/tex] when [tex]\( w = -5 \)[/tex] by following these steps:
1. Substitute [tex]\( w = -5 \)[/tex] into the expression:
[tex]\[
(-5)^2 + 3(-5) - 11
\][/tex]
2. Calculate each term separately:
- [tex]\( (-5)^2 = 25 \)[/tex]
- [tex]\( 3(-5) = -15 \)[/tex]
- The constant term is [tex]\(-11\)[/tex]
3. Combine these results:
[tex]\[
25 + (-15) - 11
\][/tex]
4. Perform the arithmetic step-by-step:
[tex]\[
25 - 15 = 10
\][/tex]
[tex]\[
10 - 11 = -1
\][/tex]
Therefore, the value of the expression when [tex]\( w = -5 \)[/tex] is [tex]\(-1\)[/tex]. The correct answer is:
[tex]\[
\boxed{-1}
\][/tex]
