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Quadratic Formula

Factorise: ...

Question

Factorise: $9 {(x - 2 y)}^{2} - 4 (x - 2 y) - 13$

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Solution

$9 {(x - 2 y)}^{2} - 4 (x - 2 y) - 13 = 0$

$= 9 (4 y^{2} - 4 y x + x^{2}) - 4 (x - 2 y) - 13$

$= 9 x^{2} - 36 y x + 36 y^{2} - 4 (x - 2 y) - 13$

$= 9 x^{2} - 36 y x + 36 y^{2} - 4 x + 8 y - 13$

$9 x^{2} - (36 y + 4) x + 36 y^{2} + 8 y - 13 = 0$

$x_{1, 2} = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$

$x = \frac{- (- 36 y - 4) \pm \sqrt{{(- 36 y - 4)}^{2} - 4 \cdot 9 (36 y^{2} + 8 y - 13)}}{2 \cdot 9}$

$x = \frac{18 y + 13}{9}, 2 y - 1$

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