To find the value of the expression \( w^2 + 3w - 11 \) when \( w = -5 \), we need to substitute \( w \) with \(-5\) and evaluate the expression. Here's the step-by-step process:
1. Start with the expression \( w^2 + 3w - 11 \).
2. Substitute \( w = -5 \) into the expression:
[tex]\[
(-5)^2 + 3(-5) - 11
\][/tex]
3. Calculate each term separately:
- The first term is \( (-5)^2 \). When you square \(-5\), you get \( 25 \), since \(-5 \times -5 = 25 \).
- The second term is \( 3(-5) \). When you multiply \( 3 \) by \(-5\), you get \( -15 \), since \( 3 \times -5 = -15 \).
- The third term is \(-11\), which remains unchanged.
4. Combine these results to get the final value:
[tex]\[
25 - 15 - 11
\][/tex]
5. Perform the arithmetic operations step-by-step:
- First, \( 25 - 15 = 10 \).
- Then, \( 10 - 11 = -1 \).
So, the value of the expression \( w^2 + 3w - 11 \) when \( w = -5 \) is \(-1\).
Therefore, the correct answer is:
D. [tex]\(-1\)[/tex]
