help algebra

2 (x^2 +3x)   = -11

2 (x+1.5)^2 = -11 + 2.25       You can finish, right?

$2x^2+6x+11$

$2\left(x^2+3x+\frac{11}{2}\right)$

$2n=3 \implies n=\frac{3}{2}$ which you want to square $\implies \left(\frac{3}{2}\right)^2$

$2\left(x^2+3x+\frac{11}{2}+\left(\frac{3}{2}\right)^2\right) =2 \left( \left(\frac{3}{2}\right)^2 \right)$

$2\left(x^2+3x+\frac{11}{2}+\left(\frac{3}{2}\right)^2-\left(\frac{3}{2}\right)^2\right)$

completing the square 

$2\left(\left(x+\frac{3}{2}\right)^2+\frac{11}{2}-\left(\frac{3}{2}\right)^2\right)   \implies  2\left(\left(x+\frac{3}{2}\right)^2\right) + 2\left( \frac{11}{2}-\frac{9}{4} \right)$

           $\Updownarrow$

$2\left(x+\frac{3}{2}\right)^2+\frac{26}{4} \equiv a(x - h)^2 + k$ 

$\overset{. \: .}{\smile }$