Solve the quadratic equation 5x^2 + 75x = 0 by factoring out the GCF.
A. The solutions are x = -15 and x = 0.
B. The solutions are x = 0 and x = 5
C. The solutions are x = -15 and x = -5
D. The solutions are x = 0 and x = 15
To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the greatest common factor (GCF), we first need to find the GCF of the terms 5x^2 and 75x. The GCF of 5x^2 and 75x is 5x.
We can factor out the GCF 5x from the equation 5x^2 + 75x = 0:
5x(x + 15) = 0.
Setting each factor equal to zero gives us:
5x = 0, which means x = 0.
x + 15 = 0, which means x = -15.
Therefore, the solution to the quadratic equation 5x^2 + 75x = 0 is x = 0 and x = -15.
The correct answer choice is A. The solutions are x = -15 and x = 0.
To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the greatest common factor (GCF), we can first factor out 5x:
5x(x + 15) = 0
Now, setting each factor equal to zero:
5x = 0 --> x = 0
x + 15 = 0 --> x = -15
Therefore, the solutions are x = 0 and x = -15.
The correct answer is option A: The solutions are x = -15 and x = 0.
To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the greatest common factor (GCF), we first need to find the GCF of the terms.
The GCF of 5x^2 and 75x is 5x. We can factor out 5x from both terms:
5x( x + 15) = 0
Now we have factored the equation. To find the solutions, we set each factor equal to zero and solve for x:
Setting 5x equal to zero:
5x = 0
Divide both sides by 5:
x = 0
Setting (x + 15) equal to zero:
x + 15 = 0
Subtract 15 from both sides:
x = -15
Therefore, the solutions to the quadratic equation are x = 0 and x = -15.
From the given options, the correct answer is A. The solutions are x = -15 and x = 0.