Solve the quadratic equation 5x2+75x=0

Question

(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.