Solve the quadratic equation 5x^2+75x=0

Question

by factoring out the GCF.(1 point)
Responses

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
.
The solutions are x equals 0 and x equals 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=−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, which is \( 5x \).

We can factor out \( 5x \):

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

Next, we set each factor equal to zero:

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

From \( 5x = 0 \):

\[ x = 0 \]

From \( x + 15 = 0 \):

\[ x = -15 \]

Thus, the solutions to the equation are:

\[ x = 0 \quad \text{and} \quad x = -15 \]

So the correct response is:

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