If x^2 + 5x = 0, then what is the value of x?

The question is asking to solve the equation x^2 + 5x = 0 for the value of x. This requires factoring the equation or applying the quadratic formula.

The solutions are $x = 0$ and $x = -5$.

Rearranging the Equation
Start with the equation given:
$$ x^2 + 5x = 0 $$
Factoring the Equation
Factor out the common term $x$:
$$ x(x + 5) = 0 $$
Applying the Zero Product Property
Set each factor equal to zero:
$$ x = 0 \quad \text{or} \quad x + 5 = 0 $$
Solving for x
From the first factor, we already have:
$$ x = 0 $$
From the second factor, solve for $x$:
$$ x + 5 = 0 \implies x = -5 $$
Final Values of x
So the solutions for the equation $x^2 + 5x = 0$ are:
$$ x = 0, \quad x = -5 $$

The solutions to the equation $x^2 + 5x = 0$ are $x = 0$ and $x = -5$.

This equation is a quadratic equation that can be solved by factoring. The two solutions represent where the parabola intersects the x-axis.

Forgetting to set both factors to zero: Ensure to use the Zero Product Property on both parts of the factored equation.
Mistaking the solutions: Check that both values found from the factors are correct and do indeed satisfy the original equation.

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