Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0 .
First, we can factor out a 2 from both terms to find the GCF:
2x² - 14x = 2(x² - 7x)
Next, we can factor out an x from the terms inside the parentheses:
2(x² - 7x) = 2x(x - 7)
Therefore, the quadratic equation 2x² - 14x = 0 can be factored as 2x(x - 7).
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we first need to find the GCF of the terms 2x^2 and -14x. The GCF in this case is 2x.
Now, we can factor out the GCF from the equation:
2x(x - 7) = 0
Now, we have a product of two factors equal to zero. According to the zero product property, for the product of two factors to be equal to zero, at least one of the factors must be equal to zero.
So, we have two possible solutions:
1. 2x = 0
Divide both sides by 2:
x = 0
2. x - 7 = 0
Add 7 to both sides:
x = 7
Therefore, the solutions to the quadratic equation 2x^2 - 14x = 0 are x = 0 and x = 7.
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we first need to identify the GCF of the terms.
The GCF of 2x^2 and -14x is 2x because both terms can be divided evenly by 2x.
Next, we factor out the GCF from the equation:
2x(x - 7) = 0
Now, we can apply the zero product property, which states that if a product of factors is equal to zero, then at least one of the factors must be zero.
This gives us two possible solutions:
1. 2x = 0
Dividing both sides by 2 gives:
x = 0
2. x - 7 = 0
Adding 7 to both sides gives:
x = 7
Therefore, the solutions to the quadratic equation 2x^2 - 14x = 0 are x = 0 and x = 7.