Let's solve the given equation step by step:

The equation is:
\[
2x - 5 = 5x + 4
\]

### Step 1: Simplify the equation
First, subtract \( 2x \) from both sides to get:
\[
-5 = 3x + 4
\]

### Step 2: Isolate the variable term
Now, subtract 4 from both sides:
\[
-5 - 4 = 3x
\]
\[
-9 = 3x
\]

### Step 3: Solve for \( x \)
Divide both sides by 3:
\[
x = \frac{-9}{3} = -3
\]

### Step 4: Find \( x^2 + x \)
Now that we know \( x = -3 \), substitute this into the expression \( x^2 + x \):
\[
x^2 + x = (-3)^2 + (-3) = 9 - 3 = 6
\]

Thus, the value of \( x^2 + x \) is:
\[
\boxed{6}
\]

Would you like more details or have any questions? Here are some related questions:

1. How do we check if the value of \( x = -3 \) is correct for the original equation?
2. How would the solution change if the equation was \( 2x - 5 = 5x - 4 \)?
3. What would happen if we had a quadratic equation instead?
4. Can we solve for \( x^2 + x \) without finding \( x \) explicitly?
5. How do we solve more complex equations involving powers of \( x \)?

**Tip:** When solving equations, always simplify step-by-step and isolate the variable carefully!

Learn how to solve the linear equation 2x – 5 = 5x + 4 and calculate x^2 + x in this step-by-step guide. This problem covers key algebraic concepts for students in Grades 6-8.

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