Solve the quadratic equation 5x2+75x=0 by factoring out the GCF.(1 point) Responses 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. The solutions are x equals negative 15 and x equals negative 5 . The solutions are x=−15 and x=0.
The quadratic equation is 5x^2 + 75x = 0.
We can factor out the greatest common factor, which is 5x:
5x(x + 15) = 0
Setting each factor equal to zero, we get:
5x = 0 or x + 15 = 0
Solving for x in each equation, we find the solutions:
x = 0 or x = -15
Therefore, the correct answer is:
The solutions are x = 0 and x = -15. (The solutions are x equals 0 and x equals negative 15.)
To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the Greatest Common Factor (GCF), we first need to identify the GCF of the terms in the equation.
In this case, the GCF of 5x^2 and 75x is 5x. By factoring out the GCF, we rewrite the equation as:
5x(x + 15) = 0
Now, we can solve for the values of x that make the equation true. Since the product of two factors equals zero, we set each factor equal to zero and solve for x.
Setting 5x = 0, we find x = 0.
Setting x + 15 = 0, we subtract 15 from both sides and get x = -15.
Therefore, the solutions to the quadratic equation 5x^2 + 75x = 0 are x = 0 and x = -15.
To solve the quadratic equation 5x^2 + 75x = 0 by factoring, we will first find the greatest common factor (GCF).
Step 1: Factor out the GCF:
The GCF of 5x^2 and 75x is 5x.
Transpose the equation:
5x(x + 15) = 0
Step 2: Set each factor equal to zero:
Setting 5x = 0, we get x = 0.
Setting (x + 15) = 0, we get x = -15.
Therefore, the solutions to the quadratic equation 5x^2 + 75x = 0 by factoring out the GCF are x = 0 and x = -15.