How do you solve the equation 5x^2 + 25x = 0?

To solve the quadratic equation 5x² + 25x = 0, we can start by factoring the equation.

First, notice that both terms on the left side are divisible by 5. We can factor out the common factor:

5(x² + 5x) = 0

Next, we can set the factor inside the parentheses equal to zero:

x² + 5x = 0

This can be further factored as:

x(x + 5) = 0

Now, we have a product of two factors equal to zero. According to the zero-product property, we can set each factor equal to zero:

• x = 0
• x + 5 = 0 which simplifies to x = -5

Thus, the solutions to the equation 5x² + 25x = 0 are:

• x = 0
• x = -5

In conclusion, the solutions we found are the points where the equation equals zero, and they can be verified by substituting back into the original equation.