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