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Solve the quadratic equation 5x2+75x=0

(1 point)
Responses

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

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

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

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

1 answer

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

  1. Factor out the common term, which is \(5x\): \[ 5x(x + 15) = 0 \]

  2. Set each factor equal to zero:

    • \(5x = 0\) gives \(x = 0\)
    • \(x + 15 = 0\) gives \(x = -15\)

Thus, the solutions to the equation are: \[ x = 0 \quad \text{and} \quad x = -15 \]

The correct response is: The solutions are \(x = 0\) and \(x = -15\).