Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x2−14x=0 .
The smaller solution is x= , and the larger solution is x= .
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we first notice that both terms have a common factor of 2x. Factoring this out, we get:
2x(x - 7) = 0
Setting each factor equal to zero, we have:
2x = 0 or x - 7 = 0
Solving for x in each equation:
For 2x = 0:
Dividing by 2 on both sides gives x = 0.
For x - 7 = 0:
Adding 7 to both sides gives 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), follow these steps:
Step 1: Find the GCF of the terms.
The GCF of 2x^2 and -14x is 2x. Factoring out 2x from the equation gives:
2x(x - 7) = 0.
Step 2: Set each factor equal to zero.
Since the product of two factors is equal to zero, you can set each factor equal to zero:
2x = 0 and (x - 7) = 0.
Step 3: Solve for x.
From the first factor, we get:
2x = 0.
Dividing both sides by 2 gives:
x = 0.
From the second factor, we get:
x - 7 = 0.
Adding 7 to both sides gives:
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 GCF, we need to find the common factor of the terms. In this case, both terms have a common factor of 2x.
Step 1: Find the GCF:
GCF of 2x^2 and -14x = 2x
Step 2: Factor out the GCF:
2x( x - 7 ) = 0
Step 3: Solve for x:
Setting each factor equal to zero gives us two possible solutions:
2x = 0 or x - 7 = 0
For the first equation, 2x = 0, divide both sides by 2 to isolate x:
x = 0
For the second equation, x - 7 = 0, add 7 to both sides to isolate x:
x = 7
So, the smaller solution is x = 0 and the larger solution is x = 7.