Question

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

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

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=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 first identify the GCF of the terms in the equation.

The GCF is \( 5x \).

Now, we can factor out \( 5x \):

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

Setting each factor equal to zero gives us:

1. \( 5x = 0 \) → \( x = 0 \)
2. \( x + 15 = 0 \) → \( x = -15 \)

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

So, the correct response is:

**The solutions are \( x = -15 \) and \( x = 0 \).**