If you are given $\displaystyle{{x}}^{{2}}+{b}{x}\usepackage{cmbright}\Huge\$ , you must add $\displaystyle{{\left(\frac{{b}}{{2}}\right)}}^{{2}}\usepackage{cmbright}\Huge\$ in order to produce a perfect square trinomial. Because $\displaystyle{b}={6}\usepackage{cmbright}\Huge\$ , add $\displaystyle{{\left(\frac{{{6}}}{{2}}\right)}}^{{2}}={{\left({3}\right)}}^{{2}}={9}\usepackage{cmbright}\Huge\$ to both sides of the equation:

$\displaystyle{{x}}^{{2}}+{6}{x}+{9}={10}+{9}\usepackage{cmbright}\Huge\$ or $\displaystyle{{x}}^{{2}}+{6}{x}+{9}={19}\usepackage{cmbright}\Huge\$