solve the following quadratic equation by factoring out the greatest common factor (GCF):2x^2 - 14x = 0
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we start by looking for the greatest common factor of the terms 2x^2 and -14x.
The GCF of 2x^2 and -14x is 2x because it is the largest factor that can divide both terms evenly.
Now, we factor out 2x from both terms:
2x^2 - 14x = 2x(x - 7)
After factoring out the GCF, the equation becomes 2x(x - 7) = 0.
The factored form of the equation is 2x(x - 7) = 0.
Now, we set each factor equal to zero and solve for x:
2x = 0 or x - 7 = 0
For the first factor, 2x = 0, we divide both sides of the equation by 2 to isolate x:
x = 0/2
The solution for the first factor is x = 0.
For the second factor, x - 7 = 0, we add 7 to both sides of the equation to isolate x:
x + 7 = 7
The solution for the second factor is x = 7.
Therefore, the solutions to the quadratic equation 2x^2 - 14x = 0 are x = 0 and x = 7.