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

Question

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

Answer 1

Let's solve the quadratic equation 5x^2 + 75x = 0 by factoring out the Greatest Common Factor (GCF):

First, identify the GCF which is 5x since both terms have 5 as a factor and at least one 'x':

5x(x + 15) = 0

Now we have two factors, 5x and (x + 15), set equal to zero. For the product of two factors to be zero, at least one of the factors must be zero.

Set each factor equal to zero and solve for x:

5x = 0 and x + 15 = 0

For the first equation (5x = 0):

x = 0 / 5
x = 0

For the second equation (x + 15 = 0):

x = -15

So the solutions to the quadratic equation 5x^2 + 75x = 0 are:

x = 0 and x = -15