Question

Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point)
Responses

The solutions are x=0 and x=15.
The solutions are x equals 0 and x equals 15 .

The solutions are x=−15 and x=−5.
The solutions are x equals negative 15 and x equals negative 5 .

The solutions are x=−15 and x=0.
The solutions are x equals negative 15 and x equals 0 .

The solutions are x=0 and x=5.

Answer 1

To solve the quadratic equation \(5x^2 + 75x = 0\) by factoring out the greatest common factor (GCF), we can follow these steps:

1. Identify the GCF of the terms in the equation. The GCF of \(5x^2\) and \(75x\) is \(5x\).
2. Factor out the GCF from the equation:

\[
5x(x + 15) = 0
\]

3. Set each factor equal to zero:

\[
5x = 0 \quad \text{or} \quad x + 15 = 0
\]

4. Solve for \(x\):

From \(5x = 0\):
\[
x = 0
\]

From \(x + 15 = 0\):
\[
x = -15
\]

Thus, the solutions to the equation are \(x = 0\) and \(x = -15\).

So the correct response is:
**The solutions are \(x = 0\) and \(x = -15\).**