solve the following quadratic equation by factoring out the greatest common factor (GCF): 2 x 2−14x=0 .(1 point) The smaller solution is x= , and the larger solution is x= .
To solve the quadratic equation by factoring out the greatest common factor (GCF), we first identify the GCF of the terms.
The two terms in the equation are 2x² and -14x. The GCF of these terms is 2x.
Next, we divide both terms by the GCF (2x) to factor it out:
(2x)(x - 7) = 0
Then, we set each factor equal to zero and solve for x:
2x = 0 → x = 0
x - 7 = 0 → x = 7
Therefore, the smaller solution is x = 0 and the larger solution is 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.
Step 1: Find the GCF of the terms 2x^2 and -14x.
The common factors of 2x^2 and -14x are 2x. Therefore, the GCF is 2x.
Step 2: Divide each term by the GCF.
Dividing both terms by 2x gives us:
(2x^2) / (2x) - (14x) / (2x) = 0
x - 7 = 0
Step 3: Solve for x.
To solve for x, we need to isolate it on one side of the equation.
Adding 7 to both sides of the equation gives us:
x - 7 + 7 = 0 + 7
x = 7
Therefore, the solutions to the quadratic equation 2x^2 - 14x = 0 are:
The smaller solution is x = 7, and the larger solution is also x = 7.
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we first need to look for common factors in the terms.
The GCF of 2x^2 and -14x is 2x. We can factor out 2x from both terms:
2x * (x - 7) = 0
Now, we can set each factor equal to zero and solve for x:
2x = 0 or (x - 7) = 0
For the first equation, dividing both sides by 2 gives us: x = 0
For the second equation, adding 7 to both sides gives us: x = 7
Therefore, the smaller solution is x = 0 and the larger solution is x = 7.