Question

Solving Quadratic Equations Using Common Factors Quick Check
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Question
Solve the quadratic equation 5x2+75x=0
by factoring out the GCF.(1 point)
Responses

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

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 start by identifying the GCF of the terms.

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

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

Next, we set each factor to zero:

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

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

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

Therefore, the correct response is:

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