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

Question

Responses

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

Answer 1

To solve the quadratic equation \(5x^2 + 75x = 0\) by factoring, we first identify the greatest common factor (GCF) of the terms.

Both terms \(5x^2\) and \(75x\) have a GCF of \(5x\). We can factor that out:

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

Now, we can set each factor equal to zero:

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

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 \(x=0\).