Add 25 to both sides: $\displaystyle{{\left({x}+{4}\right)}}^{{2}}={50}\usepackage{cmbright}\Huge\$

Use the Square Root Property: $\displaystyle{x}+{4}=\pm\sqrt{{50}}\usepackage{cmbright}\Huge\$

Solve for x: $\displaystyle{x}=-{4}\pm\sqrt{{50}}\usepackage{cmbright}\Huge\$

Simplify the radical: $\displaystyle{x}=-{4}\pm\sqrt{{{25}\cdot{2}}}=-{4}\pm{5}\sqrt{{2}}\usepackage{cmbright}\Huge\$