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
