Question

Solve the equation by completing the square. 3x^2 -6+9=0

Answer 1

The factored form would be (3x-9)(x-1)
The picture should help a bit

Answer 2

Divide through by 3:

$\frac{3x^2 -6x+9}{3} = \frac{0}{3} \newline \newline x^2 -2x+3=0$

Complete the square:

$x^2 -2x +1+3=+1$

$(x-1)^2+3=+1$

$(x-1)^2=-2$

$x-1= \sqrt{-2}$

$x=-\sqrt{2} i+1$

$x=\sqrt{2} i+1$