Question

Solve the quadratic equation 5x2+75x=0
(1 point)
Responses

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

The solutions are x=-5 and x=-15
The solutions are x=-5 and x=-15

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

The solutions are x=0 and x=-15

Answer 1

To solve the quadratic equation \( 5x^2 + 75x = 0 \), we can factor out the common term:

1. Factor out \( 5x \):
\[
5x(x + 15) = 0
\]

2. Set each factor to zero:
\[
5x = 0 \quad \text{or} \quad x + 15 = 0
\]

3. Solving these gives:
\[
x = 0 \quad \text{or} \quad x = -15
\]

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

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