Answer
$x = ±2$
Work Step by Step
$2^{x^{2}+6} = 1024$
$2^{x^{2}+6} = 2^{10}$
$x^{2} + 6 = 10$
$x^{2} = 10 - 6$
$x^{2} = 4$
$x = ±\sqrt 4$
$x = ±2$
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