Solve the Equation: Finding x in x² + x = 0

To solve this problem, we'll follow these steps:

• Step 1: Factor the equation $x^2 + x = 0$.
• Step 2: Use the Zero-Product Property to solve for $x$.

Now, let's work through each step:

Step 1: Start by factoring the left-hand side of the equation:
$x^2 + x = x(x + 1)$

Step 2: Apply the Zero-Product Property:
Since $x(x + 1) = 0$, we have two possible equations:
1) $x = 0$
2) $x + 1 = 0$

For the second equation, solve for $x$:
$x + 1 = 0$ implies $x = -1$

Therefore, the solutions to the equation are $x = 0$ and $x = -1$.

Hence, the value of the parameter $x$ is $x = 0, x = -1$.