Solve x/1.06^8+1000/1.06+4000/1.06^2-10000/1.06^7=0

$$\frac { x } { 1.06 ^ { 8 } } + \frac { 1000 } { 1.06 } + \frac { 4000 } { 1.06 ^ { 2 } } - \frac { 10000 } { 1.06 ^ { 7 } } = 0$$

Solve for x

$$x=3422.29329198464$$

Steps for Solving Linear Equation

Calculate 1.06 to the power of 8 and get 1.5938480745308416.

$$\frac{x}{1.5938480745308416}+\frac{1000}{1.06}+\frac{4000}{1.06^{2}}-\frac{10000}{1.06^{7}}=0$$

Expand \frac{1000}{1.06} by multiplying both numerator and the denominator by 100.

$$\frac{x}{1.5938480745308416}+\frac{100000}{106}+\frac{4000}{1.06^{2}}-\frac{10000}{1.06^{7}}=0$$

Reduce the fraction \frac{100000}{106} to lowest terms by extracting and canceling out 2.

$$\frac{x}{1.5938480745308416}+\frac{50000}{53}+\frac{4000}{1.06^{2}}-\frac{10000}{1.06^{7}}=0$$

Calculate 1.06 to the power of 2 and get 1.1236.

$$\frac{x}{1.5938480745308416}+\frac{50000}{53}+\frac{4000}{1.1236}-\frac{10000}{1.06^{7}}=0$$

Expand \frac{4000}{1.1236} by multiplying both numerator and the denominator by 10000.

$$\frac{x}{1.5938480745308416}+\frac{50000}{53}+\frac{40000000}{11236}-\frac{10000}{1.06^{7}}=0$$

Reduce the fraction \frac{40000000}{11236} to lowest terms by extracting and canceling out 4.

$$\frac{x}{1.5938480745308416}+\frac{50000}{53}+\frac{10000000}{2809}-\frac{10000}{1.06^{7}}=0$$

Least common multiple of 53 and 2809 is 2809. Convert \frac{50000}{53} and \frac{10000000}{2809} to fractions with denominator 2809.

$$\frac{x}{1.5938480745308416}+\frac{2650000}{2809}+\frac{10000000}{2809}-\frac{10000}{1.06^{7}}=0$$

Since \frac{2650000}{2809} and \frac{10000000}{2809} have the same denominator, add them by adding their numerators.

$$\frac{x}{1.5938480745308416}+\frac{2650000+10000000}{2809}-\frac{10000}{1.06^{7}}=0$$

Add 2650000 and 10000000 to get 12650000.

$$\frac{x}{1.5938480745308416}+\frac{12650000}{2809}-\frac{10000}{1.06^{7}}=0$$

Calculate 1.06 to the power of 7 and get 1.50363025899136.

$$\frac{x}{1.5938480745308416}+\frac{12650000}{2809}-\frac{10000}{1.50363025899136}=0$$

Expand \frac{10000}{1.50363025899136} by multiplying both numerator and the denominator by 100000000000000.

$$\frac{x}{1.5938480745308416}+\frac{12650000}{2809}-\frac{1000000000000000000}{150363025899136}=0$$

Reduce the fraction \frac{1000000000000000000}{150363025899136} to lowest terms by extracting and canceling out 128.

$$\frac{x}{1.5938480745308416}+\frac{12650000}{2809}-\frac{7812500000000000}{1174711139837}=0$$

Least common multiple of 2809 and 1174711139837 is 1174711139837. Convert \frac{12650000}{2809} and \frac{7812500000000000}{1174711139837} to fractions with denominator 1174711139837.

$$\frac{x}{1.5938480745308416}+\frac{5290172986450000}{1174711139837}-\frac{7812500000000000}{1174711139837}=0$$

Since \frac{5290172986450000}{1174711139837} and \frac{7812500000000000}{1174711139837} have the same denominator, subtract them by subtracting their numerators.

$$\frac{x}{1.5938480745308416}+\frac{5290172986450000-7812500000000000}{1174711139837}=0$$

Subtract 7812500000000000 from 5290172986450000 to get -2522327013550000.

$$\frac{x}{1.5938480745308416}-\frac{2522327013550000}{1174711139837}=0$$

Add \frac{2522327013550000}{1174711139837} to both sides. Anything plus zero gives itself.

$$\frac{x}{1.5938480745308416}=\frac{2522327013550000}{1174711139837}$$

Multiply both sides by 1.5938480745308416.

$$x=\frac{2522327013550000}{1174711139837}\times 1.5938480745308416$$

Convert decimal number 1.5938480745308416 to fraction \frac{249038761645444}{10000000000}. Reduce the fraction \frac{249038761645444}{10000000000} to lowest terms by extracting and canceling out 4.

$$x=\frac{2522327013550000}{1174711139837}\times \frac{62259690411361}{39062500000000}$$

Multiply \frac{2522327013550000}{1174711139837} times \frac{62259690411361}{39062500000000} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{2522327013550000\times 62259690411361}{1174711139837\times 39062500000000}$$

Do the multiplications in the fraction \frac{2522327013550000\times 62259690411361}{1174711139837\times 39062500000000}.

$$x=\frac{157039298979835762120941550000}{45887153899882812500000000}$$

Reduce the fraction \frac{157039298979835762120941550000}{45887153899882812500000000} to lowest terms by extracting and canceling out 58735556991850000.

$$x=\frac{2673666634363}{781250000}$$