Answer
$x \approx ±2.449$
Work Step by Step
$(\frac{1}{2})^{-x^{2} +4} = 4$
$(2^{-1})^{-x^{2} +4} = 2^{2}$
$2^{x^{2} -4} = 2^{2}$
$x^{2} - 4 = 2$
$x^{2} = 2 + 4$
$x^{2} = 6$
$x = ±\sqrt 6$
$x \approx ±2.449$
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