Solve x(1.0225^60-1/0.0225)=3000(1.093^3-1/0.093(1.093)^3)+3000

$$x ( \frac { 1.0225 ^ { 60 } - 1 } { 0.0225 } ) = 3000 ( \frac { 1.093 ^ { 3 } - 1 } { 0.093 ( 1.093 ) ^ { 3 } } ) + 3000$$

Evaluate

$$\frac{13780201071000}{1305751357}\approx 10553.464866895$$

Solution Steps

Calculate 1.093 to the power of 3 and get 1.305751357.

$$3000\times \frac{1.305751357-1}{0.093\times 1.093^{3}}+3000$$

Subtract 1 from 1.305751357 to get 0.305751357.

$$3000\times \frac{0.305751357}{0.093\times 1.093^{3}}+3000$$

Calculate 1.093 to the power of 3 and get 1.305751357.

$$3000\times \frac{0.305751357}{0.093\times 1.305751357}+3000$$

Multiply 0.093 and 1.305751357 to get 0.121434876201.

$$3000\times \frac{0.305751357}{0.121434876201}+3000$$

Expand \frac{0.305751357}{0.121434876201} by multiplying both numerator and the denominator by 1000000000000.

$$3000\times \frac{305751357000}{121434876201}+3000$$

Reduce the fraction \frac{305751357000}{121434876201} to lowest terms by extracting and canceling out 93.

$$3000\times \frac{3287649000}{1305751357}+3000$$

Express 3000\times \frac{3287649000}{1305751357} as a single fraction.

$$\frac{3000\times 3287649000}{1305751357}+3000$$

Multiply 3000 and 3287649000 to get 9862947000000.

$$\frac{9862947000000}{1305751357}+3000$$

Convert 3000 to fraction \frac{3917254071000}{1305751357}.

$$\frac{9862947000000}{1305751357}+\frac{3917254071000}{1305751357}$$

Since \frac{9862947000000}{1305751357} and \frac{3917254071000}{1305751357} have the same denominator, add them by adding their numerators.

$$\frac{9862947000000+3917254071000}{1305751357}$$

Add 9862947000000 and 3917254071000 to get 13780201071000.

$$\frac{13780201071000}{1305751357}$$

Factor

$$\frac{3 \cdot 7 \cdot 13 \cdot 17 \cdot 23 \cdot 129097 \cdot 2 ^ {3} \cdot 5 ^ {3}}{1093 ^ {3}} = 10553\frac{607000579}{1305751357} = 10553.464866895023$$