Completar la calculadora cuadrada

Cuadrados completos paso a paso

La calculadora intentará completar el cuadrado para la expresión cuadrática dada, elipse, hipérbola o cualquier expresión polinomial, con los pasos que se muestran.

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