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Quadratic Formula

Solve the equ...

Question

Solve the equation: $2 {(x - 3)}^{2} + 3 (x - 2) (2 x - 3) = 8 (x + 4) (x - 4) - 1$

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Solution

According to question,

$2 (x - 3)^{2} + 3 (x - 2) (2 x - 3) = 8 (x + 4) (x - 4) - 1$

$\Rightarrow 2 (x^{2} - 6 x + 9) + 3 (2 x^{2} - 7 x + 6) = 8 (x^{2} - 16) - 1$

$\Rightarrow 2 x^{2} - 12 x + 18 + 6 x^{2} - 21 x + 18 = 8 x^{2} - 128 - 1$

$\Rightarrow 165 = 33 x$

$\Rightarrow x = \frac{165}{33}$

$\Rightarrow x = 5$

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