Rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x2=22x
The smaller solution is x= , and the larger solution is x= .
The equation is already in standard form.
Now let's solve by factoring out the GCF.
First, subtract 22x from both sides:
6x^2 - 22x = 0
Now, let's factor out the GCF, which is 2x:
2x(3x - 11) = 0
Now we have two factors equal to zero:
2x = 0 or 3x - 11 = 0
From the first factor:
2x = 0
x = 0
From the second factor:
3x - 11 = 0
3x = 11
x = 11/3
The smaller solution is x = 0, and the larger solution is x = 11/3.
To rewrite the quadratic equation in standard form, we need to move all the terms to one side of the equation.
Starting with the given equation: 6x^2 = 22x
Subtracting 22x from both sides, we get: 6x^2 - 22x = 0
Next, we need to factor out the greatest common factor (GCF), which is 2x in this case:
2x(3x - 11) = 0
Now we can solve for x by setting each factor equal to zero:
2x = 0 or 3x - 11 = 0
For the first equation, dividing both sides by 2, we get x = 0.
For the second equation, adding 11 to both sides: 3x = 11. Then, dividing both sides by 3, we have x = 11/3.
Thus, the smaller solution is x = 0, and the larger solution is x = 11/3.
To rewrite the quadratic equation in standard form, we need to move all the terms to one side of the equation so that it is in the form "ax^2 + bx + c = 0". Let's start by subtracting 22x from both sides of the equation:
6x^2 - 22x = 0
Now, we have the equation in standard form. To solve it by factoring out the greatest common factor (GCF), we need to find the GCF of the terms on the left side of the equation. In this case, both terms have a common factor of 2x:
2x(3x - 11) = 0
Now, we can set each factor equal to zero and solve for x:
2x = 0, which gives x = 0
3x - 11 = 0, solving for x:
3x = 11
x = 11/3
Therefore, the smaller solution is x = 0, and the larger solution is x = 11/3.