[tex]x_1+x_2=-\dfrac{b}{a}=-k\\
x_1x_2=\dfrac{c}{a}=54\\
x_1=2x_2\\\\
2x_2+x_2=-k\\
3x_2=-k\\
x_2=-\dfrac{k}{3}\\\\
2x_2\cdot x_2=54\\
2x_2^2=54\\
x_2^2=27\\\\ \left(-\dfrac{k}{3}\right)^2=27\\
\dfrac{k^2}{9}=27\\
k^2=243\\
k=\pm\sqrt{243}\\
k\approx\pm15.6
[/tex]