we have
[tex]x^{2}=9x+ 6[/tex]
Group terms that contain the same variable, and move the constant to the opposite side of the equation
[tex]x^{2}-9x=6[/tex]
Complete the square. Remember to balance the equation by adding the same constants to each side
[tex]x^{2}-9x+4.5^{2}=6+4.5^{2}[/tex]
[tex]x^{2}-9x+20.25=6+20.25[/tex]
[tex]x^{2}-9x+20.25=26.25[/tex]
Rewrite as perfect squares
[tex](x-4.5)^{2}=26.25[/tex]
[tex](x-4.5)=(+/-)\sqrt{26.25}\\ \\x1=4.5+\sqrt{26.25}=9.623\\x2=4.5-\sqrt{26.25}=-0.623[/tex]
therefore
the answer is
[tex]x1=4.5+\sqrt{26.25}=9.623[/tex]
[tex]x2=4.5-\sqrt{26.25}=-0.623[/tex]
