rewrite the following quadratic equation in standard form and then solve by factoring out the GCF: 6x^2 = 22x
To rewrite the quadratic equation in standard form, we start by moving all the terms to one side of the equation. So, we subtract 22x from both sides:
6x^2 - 22x = 0
Now, we can factor out the greatest common factor (GCF), which is 2x:
2x(3x - 11) = 0
Next, we set each factor equal to zero and solve for x:
2x = 0 or 3x - 11 = 0
For 2x = 0, we divide by 2 to isolate x:
x = 0
For 3x - 11 = 0, we add 11 to both sides and then divide by 3:
3x = 11
x = 11/3
So, the solutions to the quadratic equation 6x^2 = 22x are x = 0 and x = 11/3.