y=1.2x^2+2x+9y=1.2x2+2x+9
First, transfer 9 to the other side of the equation.
y-9=1.2x^2+2xy−9=1.2x2+2x
Factor out the coefficient of x^2x2.
y-9=1.2(x^2+(2x)/1.2)y−9=1.2(x2+2x1.2)
y-9=1.2(x^2+5/3x)y−9=1.2(x2+53x)
Now, we will compute for the value that we can add to x^2+5/3xx2+53x to make it a perfect square. Divide the coefficient of xx by 2 and multiply it by itself.
5/3÷2=5/653÷2=56
(5/6)(5/6)=25/36(56)(56)=2536
Add 25/362536 inside the parentheses. We must also add 1.2(25/36)1.2(2536) to the other side to maintain equality.
y-9+1.2(25/36)=1.2(x^2+5/3x+25/36)y−9+1.2(2536)=1.2(x2+53x+2536)
y-9+5/6=1.2(x^2+5/3x+25/36)y−9+56=1.2(x2+53x+2536)
y-49/6=1.2(x^2+5/3x+25/36)y−496=1.2(x2+53x+2536)
Factor out x^2+5/3x+25/36x2+53x+2536. 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−496=1.2(x+56)(x+56)
y-49/6=1.2(x+5/6)^2y−496=1.2(x+56)2
Transfer 49/6496 to the other side of the equation then you're done.
y=1.2(x+5/6)^2+49/6y=1.2(x+56)2+496
