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

Question

by factoring out the GCF.(1 point)
Responses

The solutions are x=−15 and x=−5

The solutions are x=0 and x=5

The solutions are x=−15 and x=0 .

The solutions are x=0 and x=15

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.

The GCF of \( 5x^2 \) and \( 75x \) is \( 5x \). We can factor this out:

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

Next, we set each factor equal to zero:

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

Solving these equations gives us:

1. From \( 5x = 0 \), we have \( x = 0 \).
2. From \( x + 15 = 0 \), we have \( x = -15 \).

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

The correct response is:

The solutions are x=−15 and x=0.