[tex]x^2-11x=x^2-2x\cdot5.5+5.5^2-5.5^2=(x-5.5)^2-30.25\\\\=(x-5.5)^2-30\dfrac{1}{4}=(x-5.5)^2-\dfrac{121}{4}\\\\\boxed{Answer:\ n=\dfrac{121}{4}}[/tex]
[tex]9x^2-21=0\ \ \ |+21\\\\9x^2=21\ \ \ \ |:9\\\\x^2=\dfrac{21}{9}\to x=\pm\sqrt{\dfrac{21}{9}}\\\\\boxed{Answer:\ 1.53,\ -1.53}[/tex]
[tex]x^2+2x=15\\\\x^2+2x\cdot1=15\ \ \ |+1^2\\\\\underbrace{x^2+2x\cdot1+1^2}_{(a+b)^2=a^2+2ab+b^2}=15+1^2\\\\(x+1)^2=16\to x+1=\pm\sqrt{16}\\\\x+1=-4\ \vee\ x+1=4\ \ \ |-1\\\\\boxed{Answer:\ x=-5,\ x=3}[/tex]
