配方法计算器

Your input: complete the square in $$$x^{2} - 2 x - 3=0$$$.

Move everything to the left side: the equation becomes $$$x^{2} - 2 x - 3=0$$$.

Proceed with the obtained expression.

Add and subtract $$$1$$$:

$$$x^{2} - 2 x - 3=x^{2} - 2 x - 3 + {\color{red}{1}} - {\color{red}{\left(1\right)}}$$$

Complete the square:

$$$-4 + {\color{red}{\left(x^{2} - 2 x + 1\right)}}=-4 + {\color{red}{\left(x - 1\right)^{2}}}$$$

Answer: $$$x^{2} - 2 x=3$$$ becomes $$$\left(x - 1\right)^{2} - 4=0$$$.