Solve the following quadratic equation by factoring out the greatest common factor (GCF): 2x^2 - 14x = 0
The smaller solution is x = _____, and the larger solution is z = ____.
To solve the equation by factoring out the greatest common factor (GCF), first we need to find the GCF of 2x^2 and -14x.
The greatest common factor is 2x. We can factor it out:
2x^2 - 14x = 2x(x - 7)
Now we have factored the equation.
To find the solutions, we set each factor equal to zero:
2x = 0
x = 0
And
x - 7 = 0
x = 7
Therefore, the smaller solution is x = 0, and the larger solution is x = 7.
Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x^2 - 22x.
The smaller solution is x = _____, and the larger solution is x = _____.
To rewrite the equation in standard form, we need to make sure the quadratic term has the highest power by rearranging the terms.
The given equation is already in standard form: 6x^2 - 22x.
To solve the equation by factoring out the greatest common factor (GCF), we need to find the GCF of 6x^2 and -22x.
The greatest common factor is 2x. We can factor it out:
6x^2 - 22x = 2x(3x - 11)
Now we have factored the equation.
To find the solutions, we set each factor equal to zero:
2x = 0
x = 0
And
3x - 11 = 0
3x = 11
x = 11/3
Therefore, the smaller solution is x = 0, and the larger solution is x = 11/3.
To solve the quadratic equation 2x^2 - 14x = 0 by factoring out the greatest common factor (GCF), we first need to determine the GCF of the terms 2x^2 and -14x. The GCF of these terms is 2x.
By factoring out the GCF, we can rewrite the equation as:
2x(x - 7) = 0
Now we set each factor equal to zero and solve for x:
1) 2x = 0
Dividing both sides by 2 gives us x = 0.
2) x - 7 = 0
Adding 7 to both sides gives us 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 need to start by factoring out the common factor of x.
Step 1: The equation 2x^2 - 14x = 0 has a common factor of x. Factoring out x, we get:
x(2x - 14) = 0
Step 2: Now we have a product of two factors equal to 0. According to the zero product property, if a product is equal to zero, then at least one of the factors must be equal to zero. Therefore, we set each factor equal to zero and solve for x:
x = 0 (Setting the first factor equal to zero)
2x - 14 = 0 (Setting the second factor equal to zero)
2x = 14
x = 7
Step 3: The solutions to the quadratic equation are x = 0 and x = 7.
The smaller solution is x = 0, and the larger solution is x = 7.