\(x^2-7x+9\)
\(=x^2-2.x.\frac{7}{2}+\left(\frac{7}{2}\right)^2-\frac{13}{4}\)
\(=\left(x-\frac{7}{2}\right)^2-\left(\frac{\sqrt{13}}{2}\right)^2\)
\(=\left(x-\frac{7}{2}-\frac{\sqrt{13}}{2}\right)\left(x-\frac{7}{2}+\frac{\sqrt{13}}{2}\right)\)
\(=\left(x-\frac{7+\sqrt{13}}{2}\right)\left(x-\frac{7-\sqrt{13}}{2}\right)\)