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Calculadora de completar o quadrado
Complete quadrados passo a passo
A calculadora tentará completar o quadrado para a expressão quadrática, elipse, hipérbole ou qualquer expressão polinomial dada, com passos mostrados.
Solution
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: $$$\frac{x^{2}}{2} + 2 x - 1=\frac{\left(x + 2\right)^{2}}{2} - 3$$$.
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