To determine the value of the expression [tex]\(w^2 + 3w - 11\)[/tex] when [tex]\(w = -5\)[/tex], follow these steps:
1. Substitute [tex]\(w\)[/tex] with [tex]\(-5\)[/tex] into the expression:
[tex]\[
w^2 + 3w - 11 \quad \text{becomes} \quad (-5)^2 + 3(-5) - 11
\][/tex]
2. Calculate the square term [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Calculate the product [tex]\(3 \times (-5)\)[/tex]:
[tex]\[
3 \times (-5) = -15
\][/tex]
4. Combine these results with [tex]\(-11\)[/tex]:
[tex]\[
25 + (-15) - 11
\][/tex]
5. Perform the addition and subtraction step-by-step:
[tex]\[
25 - 15 - 11 = 10 - 11 = -1
\][/tex]
So, the value of the expression [tex]\(w^2 + 3w - 11\)[/tex] when [tex]\(w = -5\)[/tex] is:
[tex]\[
\boxed{-1}
\][/tex]
The correct answer is D. -1.
