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

Question

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

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

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 \(5x^2\) and \(75x\), which is \(5x\).

Now we can factor the equation:

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

Setting each factor equal to zero gives us:

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

Thus, the solutions to the equation are:

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

So the correct response is:

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