Question

Solve the quadratic equation 5x2+75x=0
5
x
2
+
75
x
=
0
by factoring out the GCF.(1 point)
Responses

The solutions are x=−15
x
=
−
15
and x=−5
x
=
−
5
.
The solutions are x equals negative 15 and x equals negative 5 .

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

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

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

Answer 1

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

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

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

Next, we set each factor equal to zero:

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

Now, we solve each equation:

1. From \(5x = 0\):
\[
x = 0
\]
2. From \(x + 15 = 0\):
\[
x = -15
\]

Thus, the solutions to the equation \(5x^2 + 75x = 0\) are:

\[
x = 0 \quad \text{and} \quad x = -15
\]

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