Find the quadratic equation for the given situation — task. Mathematics CBSE, Class 10.

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The area of the following figure is \(64 \ cm^2\). We would like to find the value of \(x\).

Choose the correct equation for the given situation.

$2 x^{2} + 8 x - 64 = 0$
$2 x^{2} - 4 x + 64 = 0$
$2 x^{2} - 64 = 0$
$2 x^{2} + 64 = 0$
$2 x^{2} - 8 x - 64 = 0$

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