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To solve this problem, we need to evaluate the expression \( x^2 + 6x + 7 \) for \( x = -5 \).

Let's go through the steps:

1. Substitute \( x = -5 \) into the expression:
   \[
   (-5)^2 + 6(-5) + 7
   \]

2. Calculate \( (-5)^2 \):
   \[
   (-5)^2 = 25
   \]

3. Calculate \( 6(-5) \):
   \[
   6 \times (-5) = -30
   \]

4. Put it all together:
   \[
   25 - 30 + 7
   \]

5. Now, add and subtract in sequence:
   \[
   25 - 30 = -5
   \]
   \[
   -5 + 7 = 2
   \]

So, the answer is:
\[
\boxed{2}
\]

Would you like further explanation on any step, or do you have additional questions?

Here are some related questions for practice:
1. Evaluate \( x^2 + 4x + 3 \) when \( x = -5 \).
2. Find the value of \( x^2 + 6x + 7 \) when \( x = 3 \).
3. Determine the result of \( x^2 + 6x - 8 \) when \( x = -5 \).
4. Evaluate the expression \( x^2 + 10x + 25 \) at \( x = -5 \).
5. Substitute \( x = 2 \) into the expression \( x^2 + 6x + 7 \) and solve.

**Tip:** Always follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) when evaluating expressions.

Evaluate the expression when x = -5 for the quadratic expression x^2 + 6x + 7.

Learn how to evaluate the quadratic expression x^2 + 6x + 7 when x equals -5 with a step-by-step solution. This problem covers algebraic concepts, including operations with integers in quadratic expressions, suitable for students in Grades 7-9.

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