Use PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
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[tex]\dfrac{1}{2}-4\left(\dfrac{1}{2}+1\right)^2=\dfrac{1}{2}-4\left(1\dfrac{1}{2}\right)^2=\dfrac{1}{2}-4\left(\dfrac{1\cdot2+1}{2}\right)^2\\\\=\dfrac{1}{2}-4\left(\dfrac{3}{2}\right)^2=\dfrac{1}{2}-4\cdot\dfrac{3^2}{2^2}=\dfrac{1}{2}-4\cdot\dfrac{9}{4}=\dfrac{1}{2}-1\cdot\dfrac{9}{1}\\\\=\dfrac{1}{2}-9=\boxed{-8\dfrac{1}{2}=-\dfrac{8\cdot2+1}{2}=\boxed{-\dfrac{17}{2}}}\to\boxed{D.}[/tex]
