Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point) Responses The solutions are x=−15 and x=−5. The solutions are x equals negative 15 and x equals negative 5 . 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 .

Question

Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point) Responses The solutions are x=−15 and x=−5. The solutions are x equals negative 15 and x equals negative 5 . 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 .

Answer 1

To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the GCF, we first need to find the greatest common factor (GCF) of the terms.

The GCF of 5x^2 and 75x is 5x.

Next, we can factor out the GCF from the equation:

5x( x + 15 ) = 0

Now, we can set each factor equal to zero and solve for x:

5x = 0 x + 15 = 0

Dividing both sides of the equation 5x = 0 by 5, we get:

x = 0

Solving the equation x + 15 = 0, we subtract 15 from both sides:

x = -15

Therefore, the solutions to the quadratic equation 5x^2 + 75x = 0 are x = 0 and x = -15.

The correct response is:

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