Solve the quadratic equation 5x2+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=15
.
The solutions are x equals 0 and x equals 15 .

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=−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 of \(5x^2\) and \(75x\) is \(5x\).

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

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

Next, we set each factor equal to zero:

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

Solving these equations:

1. From \(5x = 0\): \[ x = 0 \]

2. From \(x + 15 = 0\): \[ x = -15 \]

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

The correct response is: The solutions are \( x = -15 \) and \( x = 0 \).