Solve 1.00510^3left(325/345-290right)+220^2-80^2/2

$$1.005 { 10 }^{ 3 } \left( \frac{ 325 }{ 345 } -290 \right) + \frac{ { 220 }^{ 2 } - { 80 }^{ 2 } }{ 2 }$$

Evaluate

$$-\frac{6198575}{23}\approx -269503.260869565$$

Solution Steps

Calculate 10 to the power of 3 and get 1000.

$$1.005\times 1000\left(\frac{325}{345}-290\right)+\frac{220^{2}-80^{2}}{2}$$

Multiply 1.005 and 1000 to get 1005.

$$1005\left(\frac{325}{345}-290\right)+\frac{220^{2}-80^{2}}{2}$$

Reduce the fraction \frac{325}{345} to lowest terms by extracting and canceling out 5.

$$1005\left(\frac{65}{69}-290\right)+\frac{220^{2}-80^{2}}{2}$$

Convert 290 to fraction \frac{20010}{69}.

$$1005\left(\frac{65}{69}-\frac{20010}{69}\right)+\frac{220^{2}-80^{2}}{2}$$

Since \frac{65}{69} and \frac{20010}{69} have the same denominator, subtract them by subtracting their numerators.

$$1005\times \frac{65-20010}{69}+\frac{220^{2}-80^{2}}{2}$$

Subtract 20010 from 65 to get -19945.

$$1005\left(-\frac{19945}{69}\right)+\frac{220^{2}-80^{2}}{2}$$

Express 1005\left(-\frac{19945}{69}\right) as a single fraction.

$$\frac{1005\left(-19945\right)}{69}+\frac{220^{2}-80^{2}}{2}$$

Multiply 1005 and -19945 to get -20044725.

$$\frac{-20044725}{69}+\frac{220^{2}-80^{2}}{2}$$

Reduce the fraction \frac{-20044725}{69} to lowest terms by extracting and canceling out 3.

$$-\frac{6681575}{23}+\frac{220^{2}-80^{2}}{2}$$

Calculate 220 to the power of 2 and get 48400.

$$-\frac{6681575}{23}+\frac{48400-80^{2}}{2}$$

Calculate 80 to the power of 2 and get 6400.

$$-\frac{6681575}{23}+\frac{48400-6400}{2}$$

Subtract 6400 from 48400 to get 42000.

$$-\frac{6681575}{23}+\frac{42000}{2}$$

Divide 42000 by 2 to get 21000.

$$-\frac{6681575}{23}+21000$$

Convert 21000 to fraction \frac{483000}{23}.

$$-\frac{6681575}{23}+\frac{483000}{23}$$

Since -\frac{6681575}{23} and \frac{483000}{23} have the same denominator, add them by adding their numerators.

$$\frac{-6681575+483000}{23}$$

Add -6681575 and 483000 to get -6198575.

$$-\frac{6198575}{23}$$

Factor

$$-\frac{6198575}{23} = -269503\frac{6}{23} = -269503.26086956525$$