Solve the quadratic equation 5x2+75x=0

Question

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

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

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

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

Answer 1

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

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

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

Now, we can set each factor equal to zero:

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

From the first equation:

\[ 5x = 0 \implies x = 0 \]

From the second equation:

\[ x + 15 = 0 \implies x = -15 \]

Thus, the solutions to the equation are:

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

The correct response is:

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