配方法计算器

Your input: complete the square in $$$\frac{x^{2}}{2} + 2 x - 1$$$.

Add and subtract $$$2$$$:

$$$\frac{x^{2}}{2} + 2 x - 1=\frac{x^{2}}{2} + 2 x - 1 + {\color{red}{\left(2\right)}} - {\color{red}{\left(2\right)}}$$$

Factor $$$\frac{1}{2}$$$:

$$$-3 + {\color{red}{\left(\frac{x^{2}}{2} + 2 x + 2\right)}}=-3 + {\color{red}{\left(\frac{x^{2} + 4 x + 4}{2}\right)}}$$$

Complete the square:

$$$-3 + \frac{{\color{red}{\left(x^{2} + 4 x + 4\right)}}}{2}=-3 + \frac{{\color{red}{\left(x + 2\right)^{2}}}}{2}$$$

Answer: $$$\frac{x^{2}}{2} + 2 x - 1=\frac{\left(x + 2\right)^{2}}{2} - 3$$$.