Solve x=100/(1.09)^2+100/(1.09)^3+100/(1.09)^4+100/(1.09)^4

$$x = \frac { 100 } { ( 1.09 ) ^ { 2 } } + \frac { 100 } { ( 1.09 ) ^ { 3 } } + \frac { 100 } { ( 1.09 ) ^ { 4 } } + \frac { 100 } { ( 1.09 ) ^ { 4 } }$$

Solve for x

$$x = \frac{42781000000}{141158161} = 303\frac{10077217}{141158161} \approx 303.071389546$$

Steps for Solving Linear Equation

Calculate 1.09 to the power of 2 and get 1.1881.

$$x=\frac{100}{1.1881}+\frac{100}{1.09^{3}}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Expand \frac{100}{1.1881} by multiplying both numerator and the denominator by 10000.

$$x=\frac{1000000}{11881}+\frac{100}{1.09^{3}}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Calculate 1.09 to the power of 3 and get 1.295029.

$$x=\frac{1000000}{11881}+\frac{100}{1.295029}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Expand \frac{100}{1.295029} by multiplying both numerator and the denominator by 1000000.

$$x=\frac{1000000}{11881}+\frac{100000000}{1295029}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Least common multiple of 11881 and 1295029 is 1295029. Convert \frac{1000000}{11881} and \frac{100000000}{1295029} to fractions with denominator 1295029.

$$x=\frac{109000000}{1295029}+\frac{100000000}{1295029}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Since \frac{109000000}{1295029} and \frac{100000000}{1295029} have the same denominator, add them by adding their numerators.

$$x=\frac{109000000+100000000}{1295029}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Add 109000000 and 100000000 to get 209000000.

$$x=\frac{209000000}{1295029}+\frac{100}{1.09^{4}}+\frac{100}{1.09^{4}}$$

Calculate 1.09 to the power of 4 and get 1.41158161.

$$x=\frac{209000000}{1295029}+\frac{100}{1.41158161}+\frac{100}{1.09^{4}}$$

Expand \frac{100}{1.41158161} by multiplying both numerator and the denominator by 100000000.

$$x=\frac{209000000}{1295029}+\frac{10000000000}{141158161}+\frac{100}{1.09^{4}}$$

Least common multiple of 1295029 and 141158161 is 141158161. Convert \frac{209000000}{1295029} and \frac{10000000000}{141158161} to fractions with denominator 141158161.

$$x=\frac{22781000000}{141158161}+\frac{10000000000}{141158161}+\frac{100}{1.09^{4}}$$

Since \frac{22781000000}{141158161} and \frac{10000000000}{141158161} have the same denominator, add them by adding their numerators.

$$x=\frac{22781000000+10000000000}{141158161}+\frac{100}{1.09^{4}}$$

Add 22781000000 and 10000000000 to get 32781000000.

$$x=\frac{32781000000}{141158161}+\frac{100}{1.09^{4}}$$

Calculate 1.09 to the power of 4 and get 1.41158161.

$$x=\frac{32781000000}{141158161}+\frac{100}{1.41158161}$$

Expand \frac{100}{1.41158161} by multiplying both numerator and the denominator by 100000000.

$$x=\frac{32781000000}{141158161}+\frac{10000000000}{141158161}$$

Since \frac{32781000000}{141158161} and \frac{10000000000}{141158161} have the same denominator, add them by adding their numerators.

$$x=\frac{32781000000+10000000000}{141158161}$$

Add 32781000000 and 10000000000 to get 42781000000.

$$x=\frac{42781000000}{141158161}$$

Assign x

$$x≔\frac{42781000000}{141158161}$$