Question

Resolver: 16x2+4y2+32x-8y=44

Answer 1

Explicación paso a paso:

$16( {x}^{2} + 2x) + 4( {y}^{2} - 2y) = 44$

$( {x}^{2} + 2x) + \frac{4}{16} ( {y}^{2} - 2y) = \frac{11}{4}$

$\frac{1}{4} ( {x}^{2} + 2x ) + \frac{1}{16} ( {y}^{2} - 2y) = \frac{11}{16}$

$\frac{1}{4} ( {x}^{2} + 2x + 1) + \frac{1}{16} ( {y}^{2} - 2y) = \frac{11}{16} + \frac{1}{4} (1)$

$\frac{1}{4} (x + 1 {)}^{2} + \frac{1}{16} ( {y}^{2} - 2y) = \frac{11}{16} + \frac{1}{4} (1)$

$\frac{1}{4} (x + 1 {)}^{2} + \frac{1}{16} ( {y}^{2} - 2y + 1) = \frac{11}{16} + \frac{1}{4} (1) + \frac{1}{16}(1)$

$\frac{1}{4} (x + 1 {)}^{2} + \frac{1}{16} (y - 1 {)}^{2} = \frac{11}{16} + \frac{1}{4} (1) + \frac{1}{16} (1)$

$\frac{1}{4} (x + 1 {)}^{2} + \frac{1}{16} (y - 1 {)}^{2} = 1$

$\frac{(x + 1 {)}^{2} }{4} = \frac{(y - 1 {)}^{2} }{16} = 1$