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Explanation:

Given, ${2^{4x}}^2$ - $2^{2x^2+x+16}$ + $2^{2x+30}$ = 0

⇒ ${\left({2^{2x}}^2\right)}^2$ - $2\times 2^{2x^2}\times 2^{x+15}$ + ${\left(2^{x+15}\right)}^2$ = 0

⇒ ${\left({2^{2x}}^2-2^{x+15}\right)}^2$ = 0

⇒ ${2^{2x}}^2$ = $2^{x+15}$

⇒ 2x² = x + 15

⇒ 2x² - x - 15 = 0

⇒ (2x + 5)(x - 3) = 0

⇒ x = -5/2 or 3.

Sum of all possible values of x = 3 + (-5/2) = 1/2

Hence, option (d).