Solve {l}{(5660-3500)^{2}*50+(4500-5660)^{2}*100+(5500-5660)^{2}*450+(6500-5660)^2*200}{+(5500-5660)^2*100+(8500-5660)^2*60+(9500-5660)^2*40}

$$\left. \begin{array}{l}{ ( 5660 - 3500 ) ^ { 2 } \times 50 + ( 4500 - 5660 ) ^ { 2 } \times 100 + ( 5500 - 5660 ) ^ { 2 } \times 450 + ( 6500 - 5660 ) ^ { 2 } \times 200 }\\{ + ( 5500 - 5660 ) ^ { 2 } \times 100 + ( 8500 - 5660 ) ^ { 2 } \times 60 + ( 9500 - 5660 ) ^ { 2 } \times 40 }\end{array} \right.$$

Sort

$$520480000,\ 1076320000$$

Solution Steps

Subtract 3500 from 5660 to get 2160.

$$sort(2160^{2}\times 50+\left(4500-5660\right)^{2}\times 100+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate 2160 to the power of 2 and get 4665600.

$$sort(4665600\times 50+\left(4500-5660\right)^{2}\times 100+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 4665600 and 50 to get 233280000.

$$sort(233280000+\left(4500-5660\right)^{2}\times 100+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 4500 to get -1160.

$$sort(233280000+\left(-1160\right)^{2}\times 100+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate -1160 to the power of 2 and get 1345600.

$$sort(233280000+1345600\times 100+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 1345600 and 100 to get 134560000.

$$sort(233280000+134560000+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Add 233280000 and 134560000 to get 367840000.

$$sort(367840000+\left(5500-5660\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 5500 to get -160.

$$sort(367840000+\left(-160\right)^{2}\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate -160 to the power of 2 and get 25600.

$$sort(367840000+25600\times 450+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 25600 and 450 to get 11520000.

$$sort(367840000+11520000+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Add 367840000 and 11520000 to get 379360000.

$$sort(379360000+\left(6500-5660\right)^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 6500 to get 840.

$$sort(379360000+840^{2}\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate 840 to the power of 2 and get 705600.

$$sort(379360000+705600\times 200,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 705600 and 200 to get 141120000.

$$sort(379360000+141120000,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Add 379360000 and 141120000 to get 520480000.

$$sort(520480000,\left(5500-5660\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 5500 to get -160.

$$sort(520480000,\left(-160\right)^{2}\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate -160 to the power of 2 and get 25600.

$$sort(520480000,25600\times 100+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 25600 and 100 to get 2560000.

$$sort(520480000,2560000+\left(8500-5660\right)^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 8500 to get 2840.

$$sort(520480000,2560000+2840^{2}\times 60+\left(9500-5660\right)^{2}\times 40)$$

Calculate 2840 to the power of 2 and get 8065600.

$$sort(520480000,2560000+8065600\times 60+\left(9500-5660\right)^{2}\times 40)$$

Multiply 8065600 and 60 to get 483936000.

$$sort(520480000,2560000+483936000+\left(9500-5660\right)^{2}\times 40)$$

Add 2560000 and 483936000 to get 486496000.

$$sort(520480000,486496000+\left(9500-5660\right)^{2}\times 40)$$

Subtract 5660 from 9500 to get 3840.

$$sort(520480000,486496000+3840^{2}\times 40)$$

Calculate 3840 to the power of 2 and get 14745600.

$$sort(520480000,486496000+14745600\times 40)$$

Multiply 14745600 and 40 to get 589824000.

$$sort(520480000,486496000+589824000)$$

Add 486496000 and 589824000 to get 1076320000.

$$sort(520480000,1076320000)$$

The list values are already in order.

$$520480000,1076320000$$

Evaluate

$$520480000,\ 1076320000$$