Solve the quadratic equation 5x^2+75x=0 by factoring out the GCF.
The solutions are x=−15 and x=0. The solutions are x equals negative 15 and x equals 0 . 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=5. The solutions are x equals 0 and x equals 5 . The solutions are x=0 and x=15. The solutions are x equals 0 and x equals 15 .
The correct answers 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 factor out an x:
x(5x + 75) = 0
Next, we can further simplify the equation by factoring out the GCF of 5:
5x(x + 15) = 0
Now, we can set each factor equal to zero and solve for x:
1) 5x = 0
Dividing both sides by 5 gives:
x = 0
2) x + 15 = 0
Subtracting 15 from both sides gives:
x = -15
Therefore, the solutions to the quadratic equation 5x^2 + 75x = 0 by factoring out the GCF are x = -15 and x = 0.
To solve the quadratic equation 5x^2 + 75x = 0 by factoring out the Greatest Common Factor (GCF), follow these steps:
Step 1: Identify the GCF of the terms in the equation.
In this case, both terms have a common factor of 5x.
Step 2: Factor out the GCF from the equation.
Divide each term by the GCF, which is 5x:
(5x^2 + 75x) / (5x) = 0
After factoring out the GCF, you get:
x(5x + 75) = 0
Step 3: Set each factor equal to zero and solve for x.
Since the product of two factors equals zero, we can apply the zero product property and set each factor equal to zero:
x = 0 (from the first factor)
5x + 75 = 0 (from the second factor)
Solving the second equation for x:
5x + 75 = 0
5x = -75
x = -75/5
x = -15
Therefore, the solutions to the quadratic equation 5x^2 + 75x = 0 are x = -15 and x = 0.