The curve with equation $$\(x^{2}-x+y^{2}=10\)$$ and the straight line with equation $$\(x-y=-4\)$$ intersect at the points $$\(A\)$$ and $$\(B\)$$. Work out the exact length of $$\(A B\)$$. Show your working clearly and give your answer in the form $$\(\frac{\sqrt{a}}{2}\)$$ where $$\(a\)$$ is an integer.

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