مثال: معادله $3x^2 + 4x - 15 = 0$ را به روش مربع کامل حل می کنیم. $3x^2 + 4x - 15 = 0 \xrightarrow{(1)} 3x^2 + 4x = 15 \xrightarrow{(2) \div 3} x^2 + \frac{4}{3}x = 5$ $\xrightarrow{(3) +(\frac{4}{9})} x^2 + \frac{4}{3}x + \frac{4}{9} = 5 + \frac{4}{9} \Rightarrow x^2 + \frac{4}{3}x + \frac{4}{9} = \frac{49}{9} \Rightarrow (x + \frac{2}{3})^2 = \frac{49}{9}$ $\Rightarrow \begin{cases} x + \frac{2}{3} = 7 \Rightarrow x = \frac{19}{3} \\ x + \frac{2}{3} = -7 \Rightarrow x = \frac{-23}{3} \end{cases}$