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=0 and x=5 . The solutions are x equals 0 and x equals 5 . The solutions are x=−15 and x=0 . The solutions are x equals negative 15 and x equals 0 . 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), follow these steps:

1. Identify the GCF of the two terms. The GCF of \( 5x^2 \) and \( 75x \) is \( 5x \).

2. Factor out \( 5x \) from the equation:
\[
5x(x + 15) = 0
\]

3. Set each factor equal to zero:
- \( 5x = 0 \) ⟹ \( x = 0 \)
- \( x + 15 = 0 \) ⟹ \( x = -15 \)

Thus, the solutions to the equation \( 5x^2 + 75x = 0 \) are \( x = 0 \) and \( x = -15 \).

Therefore, the correct response is:
**The solutions are x = -15 and x = 0.**