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x^2 = \left( \sqrt{7 + 2\sqrt{10}} + \sqrt{7 - 2\sqrt{10}} \right)^2 = (7 + 2\sqrt{10}) + (7 - 2\sqrt{10}) + 2\sqrt{(7 + 2\sqrt{10})(7 - 2\sqrt{10})}
x^2 = 14 + 2\sqrt{7^2 - (2\sqrt{10})^2} = 14 + 2\sqrt{49 - 40} = 14 + 2\sqrt{9} = 14 + 2 \times 3 = 14 + 6 = 20
Thus, $ x^2 = \boxed{20} $.

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