Quadratic With Inequality Insane Level!

Algebra Level 5

The values of \(k\) for which the inequality \(\dfrac{x^2+k^2}{k \cdot (x+6)} \geq 1\) is satisfied by all \(x \in (-1,1)\) are \([a, \infty)\).

Find the value of \(a\) (round off up to 3 decimal places).

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