Final answer:
To rewrite the quadratic equation in vertex form a(x-h)^2=k, we complete the square by adding the square of half the coefficient of x to both sides after factoring out the leading coefficient.
Step-by-step explanation:
To rewrite the equation 3x^2-6x=4 in the form a(x-h)^2=k, we must complete the square. First, we will move the constant term to the right side of the equation:
3x^2 - 6x - 4 = 0
Next, we factor out the coefficient of the x^2 term from the x terms on the left side:
3(x^2 - 2x) = 4
To complete the square, we take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x is -2, half of it is -1, and squaring it gives us 1. We then add 3(1) to bother sides to keep the equation balanced:
3(x^2 - 2x + 1) = 4 + 3(1)
3(x - 1)^2 = 7
Finally, we have the equation in the form a(x-h)^2=k:
(x - 1)^2 = \frac{7}{3}