Solve f(400)=(400)^3/3060000-3(400)^2/2125+108367(400)/60000+932

$$f ( 400 ) = \frac { ( 400 ) ^ { 3 } } { 3060000 } - \frac { 3 ( 400 ) ^ { 2 } } { 2125 } + \frac { 108367 ( 400 ) } { 60000 } + 932$$

Evaluate

$$\frac{11088517}{7650}\approx 1449.479346405$$

Solution Steps

Calculate 400 to the power of 3 and get 64000000.

$$\frac{64000000}{3060000}-\frac{3\times 400^{2}}{2125}+\frac{108367\times 400}{60000}+932$$

Reduce the fraction \frac{64000000}{3060000} to lowest terms by extracting and canceling out 20000.

$$\frac{3200}{153}-\frac{3\times 400^{2}}{2125}+\frac{108367\times 400}{60000}+932$$

Calculate 400 to the power of 2 and get 160000.

$$\frac{3200}{153}-\frac{3\times 160000}{2125}+\frac{108367\times 400}{60000}+932$$

Multiply 3 and 160000 to get 480000.

$$\frac{3200}{153}-\frac{480000}{2125}+\frac{108367\times 400}{60000}+932$$

Reduce the fraction \frac{480000}{2125} to lowest terms by extracting and canceling out 125.

$$\frac{3200}{153}-\frac{3840}{17}+\frac{108367\times 400}{60000}+932$$

Least common multiple of 153 and 17 is 153. Convert \frac{3200}{153} and \frac{3840}{17} to fractions with denominator 153.

$$\frac{3200}{153}-\frac{34560}{153}+\frac{108367\times 400}{60000}+932$$

Since \frac{3200}{153} and \frac{34560}{153} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3200-34560}{153}+\frac{108367\times 400}{60000}+932$$

Subtract 34560 from 3200 to get -31360.

$$-\frac{31360}{153}+\frac{108367\times 400}{60000}+932$$

Multiply 108367 and 400 to get 43346800.

$$-\frac{31360}{153}+\frac{43346800}{60000}+932$$

Reduce the fraction \frac{43346800}{60000} to lowest terms by extracting and canceling out 400.

$$-\frac{31360}{153}+\frac{108367}{150}+932$$

Least common multiple of 153 and 150 is 7650. Convert -\frac{31360}{153} and \frac{108367}{150} to fractions with denominator 7650.

$$-\frac{1568000}{7650}+\frac{5526717}{7650}+932$$

Since -\frac{1568000}{7650} and \frac{5526717}{7650} have the same denominator, add them by adding their numerators.

$$\frac{-1568000+5526717}{7650}+932$$

Add -1568000 and 5526717 to get 3958717.

$$\frac{3958717}{7650}+932$$

Convert 932 to fraction \frac{7129800}{7650}.

$$\frac{3958717}{7650}+\frac{7129800}{7650}$$

Since \frac{3958717}{7650} and \frac{7129800}{7650} have the same denominator, add them by adding their numerators.

$$\frac{3958717+7129800}{7650}$$

Add 3958717 and 7129800 to get 11088517.

$$\frac{11088517}{7650}$$

Factor

$$\frac{11 \cdot 107 \cdot 9421}{2 \cdot 3 ^ {2} \cdot 5 ^ {2} \cdot 17} = 1449\frac{3667}{7650} = 1449.4793464052289$$