Solve the Quadratic Equation: 5x^2 + 10x = 0 Using Factoring

To solve the quadratic equation $5x^2 + 10x = 0$, we will follow these steps:

• Step 1: Factor the equation: Identify the greatest common factor, which in this case is $5x$.
• Step 2: Apply the zero product property: Set each factor equal to zero and solve for $x$.

Now, let's execute these steps:

Step 1: Factor the equation.
The equation is $5x^2 + 10x = 0$.
Factor out the greatest common factor, $5x$, from both terms:
$5x(x + 2) = 0$.

Step 2: Apply the zero product property.
According to this property, if the product of factors is zero, then at least one of the factors must be zero.
Thus, we set each factor equal to zero:

• $5x = 0$
• $x + 2 = 0$

Solving these, we find:

$5x = 0 \Rightarrow x = 0$

$x + 2 = 0 \Rightarrow x = -2$

Therefore, the solutions to the equation $5x^2 + 10x = 0$ are $x_1 = 0$ and $x_2 = -2$.

The correct choice among the provided options is: $x_1 = 0, x_2 = -2$.