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

Question

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=0 and x=5.
The solutions are x equals 0 and x equals 5 .

The solutions are x=−15 and x=0.

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 \( 5x \).

Factoring this out gives us:

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

Now, we can set each factor equal to zero:

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

Thus, the solutions to the equation are:

• \( x = 0 \)
• \( x = -15 \)

The correct response is:

The solutions are x=−15 and x=0.