Enter an expression:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

### Solution

Your input: complete the square in $x^{2} - 4 x + 5 y^{2} + 10 y + 14$.

Add and subtract $5$:

$x^{2} - 4 x + 5 y^{2} + 10 y + 14=x^{2} - 4 x + 5 y^{2} + 10 y + 14 + {\color{red}{\left(5\right)}} - {\color{red}{\left(5\right)}}$

Factor $5$:

$x^{2} - 4 x + 9 + {\color{red}{\left(5 y^{2} + 10 y + 5\right)}}=x^{2} - 4 x + 9 + {\color{red}{\left(5 \left(y^{2} + 2 y + 1\right)\right)}}$

Complete the square:

$x^{2} - 4 x + 9 + 5 {\color{red}{\left(y^{2} + 2 y + 1\right)}}=x^{2} - 4 x + 9 + 5 {\color{red}{\left(y + 1\right)^{2}}}$

Add and subtract $4$:

$x^{2} - 4 x + 5 \left(y + 1\right)^{2} + 9=x^{2} - 4 x + 5 \left(y + 1\right)^{2} + 9 + {\color{red}{\left(4\right)}} - {\color{red}{\left(4\right)}}$

Complete the square:

$5 \left(y + 1\right)^{2} + 5 + {\color{red}{\left(x^{2} - 4 x + 4\right)}}=5 \left(y + 1\right)^{2} + 5 + {\color{red}{\left(x - 2\right)^{2}}}$

Answer: $x^{2} - 4 x + 5 y^{2} + 10 y + 14=\left(x - 2\right)^{2} + 5 \left(y + 1\right)^{2} + 5$.