配方法计算器
逐步配方
该计算器将尝试对给定的二次表达式、椭圆、双曲线或任意多项式表达式进行配方，并显示步骤。
Solution
Your input: complete the square in $$$x^{2} - 4 x + 5 y^{2} + 10 y + 14$$$.
Add and subtract $$$4$$$:
$$$x^{2} - 4 x + 5 y^{2} + 10 y + 14=x^{2} - 4 x + 5 y^{2} + 10 y + 14 + {\color{red}{\left(4\right)}} - {\color{red}{\left(4\right)}}$$$
Complete the square:
$$$5 y^{2} + 10 y + 10 + {\color{red}{\left(x^{2} - 4 x + 4\right)}}=5 y^{2} + 10 y + 10 + {\color{red}{\left(x - 2\right)^{2}}}$$$
Add and subtract $$$5$$$:
$$$5 y^{2} + 10 y + \left(x - 2\right)^{2} + 10=5 y^{2} + 10 y + \left(x - 2\right)^{2} + 10 + {\color{red}{\left(5\right)}} - {\color{red}{\left(5\right)}}$$$
Factor $$$5$$$:
$$$\left(x - 2\right)^{2} + 5 + {\color{red}{\left(5 y^{2} + 10 y + 5\right)}}=\left(x - 2\right)^{2} + 5 + {\color{red}{\left(5 \left(y^{2} + 2 y + 1\right)\right)}}$$$
Complete the square:
$$$\left(x - 2\right)^{2} + 5 + 5 {\color{red}{\left(y^{2} + 2 y + 1\right)}}=\left(x - 2\right)^{2} + 5 + 5 {\color{red}{\left(y + 1\right)^{2}}}$$$
Answer: $$$x^{2} - 4 x + 5 y^{2} + 10 y + 14=\left(x - 2\right)^{2} + 5 \left(y + 1\right)^{2} + 5$$$.