4x2 + y2 + 12x + 4y + 13
= 4x2 + 12x + 9 + y2 + 4y + 4
= (2x + 3)2 + (y + 2)2
\(4x^2+y^2+12x+4y+13\)
\(=4x^2+12x+9+y^2+4y+4\)
\(=\left(2x\right)^2+2.2x.3+3^2+y^2+2.y.2+4\)
\(=\left(2x+3\right)^2+\left(y+2\right)^2\)
\(4x^2+y^2+12x+4y+13\)
\(=4x^2+12x+9+y^2+4y+4\)
\(=\left(2x+3\right)^2+\left(y+2\right)^2\)