Solve 11left(16^2-16right)+12left(16^3-1right)=xleft(16^5-16^2right)+13left({16}^4-16right)+14({16}^3-1)+2400

$$11 \left( { 16 }^{ 2 } -16 \right) +12 \left( { 16 }^{ 3 } -1 \right) = x \left( { 16 }^{ 5 } - { 16 }^{ 2 } \right) +13 \left( { 16 }^{ 4 } -16 \right) +14( { 16 }^{ 3 } -1)+2400$$

Solve for x

$$x=-\frac{28657}{34944}\approx -0.820083562$$

Steps for Solving Linear Equation

Calculate 16 to the power of 2 and get 256.

$$11\left(256-16\right)+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Subtract 16 from 256 to get 240.

$$11\times 240+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Multiply 11 and 240 to get 2640.

$$2640+12\left(16^{3}-1\right)=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Calculate 16 to the power of 3 and get 4096.

$$2640+12\left(4096-1\right)=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Subtract 1 from 4096 to get 4095.

$$2640+12\times 4095=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Multiply 12 and 4095 to get 49140.

$$2640+49140=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Add 2640 and 49140 to get 51780.

$$51780=x\left(16^{5}-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Calculate 16 to the power of 5 and get 1048576.

$$51780=x\left(1048576-16^{2}\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Calculate 16 to the power of 2 and get 256.

$$51780=x\left(1048576-256\right)+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Subtract 256 from 1048576 to get 1048320.

$$51780=x\times 1048320+13\left(16^{4}-16\right)+14\left(16^{3}-1\right)+2400$$

Calculate 16 to the power of 4 and get 65536.

$$51780=x\times 1048320+13\left(65536-16\right)+14\left(16^{3}-1\right)+2400$$

Subtract 16 from 65536 to get 65520.

$$51780=x\times 1048320+13\times 65520+14\left(16^{3}-1\right)+2400$$

Multiply 13 and 65520 to get 851760.

$$51780=x\times 1048320+851760+14\left(16^{3}-1\right)+2400$$

Calculate 16 to the power of 3 and get 4096.

$$51780=x\times 1048320+851760+14\left(4096-1\right)+2400$$

Subtract 1 from 4096 to get 4095.

$$51780=x\times 1048320+851760+14\times 4095+2400$$

Multiply 14 and 4095 to get 57330.

$$51780=x\times 1048320+851760+57330+2400$$

Add 851760 and 57330 to get 909090.

$$51780=x\times 1048320+909090+2400$$

Add 909090 and 2400 to get 911490.

$$51780=x\times 1048320+911490$$

Swap sides so that all variable terms are on the left hand side.

$$x\times 1048320+911490=51780$$

Subtract 911490 from both sides.

$$x\times 1048320=51780-911490$$

Subtract 911490 from 51780 to get -859710.

$$x\times 1048320=-859710$$

Divide both sides by 1048320.

$$x=\frac{-859710}{1048320}$$

Reduce the fraction \frac{-859710}{1048320} to lowest terms by extracting and canceling out 30.

$$x=-\frac{28657}{34944}$$