[tex]\bf 2x^2+16x-y+31=0\implies 2x^2+16x+31=y
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2x(x+8)+31=y
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\textit{now, let's make 2x = t}\implies t(x+8)+31=y
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\textit{since we know 2x=t, then }\boxed{x=\cfrac{t}{2}}
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\textit{and thus }x+8\implies \cfrac{t}{2}+8\implies t\left( \cfrac{t}{2}+8 \right)+31=y
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\boxed{\cfrac{t^2}{2}+8t+31=y}[/tex]
