#y=1.2x^2+2x+9#
First, transfer 9 to the other side of the equation.
#y-9=1.2x^2+2x#
Factor out the coefficient of #x^2#.
#y-9=1.2(x^2+(2x)/1.2)#
#y-9=1.2(x^2+5/3x)#
Now, we will compute for the value that we can add to #x^2+5/3x# to make it a perfect square. Divide the coefficient of #x# by 2 and multiply it by itself.
#5/3÷2=5/6#
#(5/6)(5/6)=25/36#
Add #25/36# inside the parentheses. We must also add #1.2(25/36)# to the other side to maintain equality.
#y-9+1.2(25/36)=1.2(x^2+5/3x+25/36)#
#y-9+5/6=1.2(x^2+5/3x+25/36)#
#y-49/6=1.2(x^2+5/3x+25/36)#
Factor out #x^2+5/3x+25/36#. We made this into a perfect square trinomial so it should be easy.
#y-49/6=1.2(x+5/6)(x+5/6)#
#y-49/6=1.2(x+5/6)^2#
Transfer #49/6# to the other side of the equation then you're done.
#y=1.2(x+5/6)^2+49/6#
