1989 AIME Problem 8

Assume that x_1,x_2,\ldots,x_7 are real numbers such that

x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1^{}_{}

4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12^{}_{}

9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123^{}_{}

Find the value of 16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7^{}.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.