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Algebra Level 4

{x1+4x2+9x3+16x4+25x5+36x6+49x7=44x1+9x2+16x3+25x4+36x5+49x6+64x7=449x1+16x2+25x3+36x4+49x5+64x6+81x7=444 \begin{cases} x_1 + 4 x_2 + 9 x_3 +16x_4 + 25x_5 + 36x_6+ 49 x_7 & = & 4 \\ 4x_1 + 9 x_2 + 16x_3 +25x_4 + 36x_5 + 49x_6 + 64 x_7 & = & 44 \\ 9 x_1 + 16 x_2 + 25 x_3 +36x_4 + 49x_5 + 64x_6 + 81 x_7 & = & 444 \\ \end{cases}

If x1,x2,,x7x_1, x_2, \ldots , x_7 satisfy the system of equations above, find the value of

16x1+25x2+36x3+49x4+64x5+81x6+100x7. 16x_{ 1 }+25x_{ 2 }+36x_{ 3 }+49{ x }_{ 4 }+64x_5 + 81x_6 +{ 100x }_{ 7 } .

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