The equation is given to be:
[tex]3x^2-12x=9[/tex]Divide each term by 3:
[tex]\begin{gathered} \frac{3x^2}{3}-\frac{12x}{3}=\frac{9}{3} \\ x^2-4x=3 \end{gathered}[/tex]Add the square of half the coefficient of x to both sides of the equation:
[tex]\begin{gathered} Coefficient=-4 \\ Half=-\frac{4}{2}=-2 \\ Square=(-2)^2 \\ \therefore \\ x^2-4x+(-2)^2=3+(-2)^2 \\ x^2-4x+(-2)^2=7 \end{gathered}[/tex]Complete the square:
[tex](x-2)^2=7[/tex]The correct option is OPTION C.
