Answer
182
Work Step by Step
Plugging in the given value of $x$ into the function, we find:
$$x+\frac{1}{2}x^4-\frac{3}{4}x^3+10,\:x=-4 \\ -4+\frac{1}{2}\left(-4\right)^4-\frac{3}{4}\left(-4\right)^3+10 \\ 182$$
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