Add $\displaystyle{{\left(\frac{{20}}{{2}}\right)}}^{{2}}={{\left({10}\right)}}^{{2}}={100}\usepackage{cmbright}\Huge\$ to both sides to complete the square: $\displaystyle{{x}}^{{2}}+{20}{x}+{100}={80}\usepackage{cmbright}\Huge\$

Write the left side as the square of a binomial: $\displaystyle{{\left({x}+{10}\right)}}^{{2}}={80}\usepackage{cmbright}\Huge\$

Take the square root of both sides: $\displaystyle{x}+{10}=\pm\sqrt{{80}}=\pm\sqrt{{{16}\cdot{5}}}=\pm{4}\sqrt{{5}}\usepackage{cmbright}\Huge\$

Solve for x: $\displaystyle{x}=-{10}\pm{4}\sqrt{{5}}\usepackage{cmbright}\Huge\$