Final answer:
To solve the quadratic equation 3x²-8x+4=0 using the box method, we need to factor by grouping. The solutions to the equation are x=2 and x=2/3.
Step-by-step explanation:
To solve the quadratic equation 3x²-8x+4=0 using the box method, we need to factor by grouping.
First, we need to multiply the coefficient of x² and the constant term, which is 3 * 4 = 12. We need to find two numbers whose product is 12 and whose sum is -8 (the coefficient of x). The numbers are -2 and -6.
Next, we group the terms and factor:
3x²-2x-6x+4=0
x(3x-2)-2(3x-2)=0
(x-2)(3x-2)=0
Setting each factor equal to zero, we find x=2 and x=2/3 as the solutions to the quadratic equation.