# Think Geometry, Not Algebra

Geometry Level 5

$\begin{eqnarray} &&2\sqrt{(x^{2}-8x+y^{2}+16)(x^{2}-6x+y^{2}-14y+58)} \\ && +2x^{2}-14x+2y^{2}-14y+74 \end{eqnarray}$

For real numbers $$x,y$$, what is the minimum value of the above expression, subject to the constraint $$3x+y-6 = 0$$?

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