To solve the expression \( 6x + x^2 - 5 \) when \( x = 3 \), we simply substitute the value of \( x \) into the equation and simplify.

1. Substitute \( x = 3 \) into the expression:

\[
6(3) + 3^2 - 5
\]

2. Now, calculate each term:

\[
6(3) = 18
\]
\[
3^2 = 9
\]

So the expression becomes:

\[
18 + 9 - 5
\]

3. Simplify further:

\[
18 + 9 = 27
\]
\[
27 - 5 = 22
\]

Thus, the value of the expression is \( 22 \).

Would you like more details on any of the steps?

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Here are 5 related questions to explore further:
1. How would the result change if \( x = -3 \)?
2. What is the result of the expression \( x^2 - 6x + 5 \) when \( x = 3 \)?
3. How would you factor the expression \( x^2 + 6x - 5 \)?
4. What is the derivative of the expression \( 6x + x^2 - 5 \)?
5. How does the value of the expression change if \( x = 0 \)?

**Tip:** Always simplify expressions step by step, handling multiplication, powers, and then addition/subtraction carefully.

Learn how to evaluate the algebraic expression 6x + x^2 - 5 for x = 3. This step-by-step solution covers key algebraic concepts like substitution and polynomial evaluation. Suitable for students in Grades 7-9.

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