Solve (0.18^2/0.26+0.18+0.05^2/0.39+0.05)*30^2/4=

$$( \frac { 0.18 ^ { 2 } } { 0.26 + 0.18 } + \frac { 0.05 ^ { 2 } } { 0.39 + 0.05 } ) * \frac { 30 ^ { 2 } } { 4 } =$$

Evaluate

$$\frac{3141}{176}\approx 17.846590909$$

Solution Steps

Calculate 0.18 to the power of 2 and get 0.0324.

$$\left(\frac{0.0324}{0.26+0.18}+\frac{0.05^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Add 0.26 and 0.18 to get 0.44.

$$\left(\frac{0.0324}{0.44}+\frac{0.05^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.0324}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{324}{4400}+\frac{0.05^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Reduce the fraction \frac{324}{4400} to lowest terms by extracting and canceling out 4.

$$\left(\frac{81}{1100}+\frac{0.05^{2}}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Calculate 0.05 to the power of 2 and get 0.0025.

$$\left(\frac{81}{1100}+\frac{0.0025}{0.39+0.05}\right)\times \frac{30^{2}}{4}$$

Add 0.39 and 0.05 to get 0.44.

$$\left(\frac{81}{1100}+\frac{0.0025}{0.44}\right)\times \frac{30^{2}}{4}$$

Expand \frac{0.0025}{0.44} by multiplying both numerator and the denominator by 10000.

$$\left(\frac{81}{1100}+\frac{25}{4400}\right)\times \frac{30^{2}}{4}$$

Reduce the fraction \frac{25}{4400} to lowest terms by extracting and canceling out 25.

$$\left(\frac{81}{1100}+\frac{1}{176}\right)\times \frac{30^{2}}{4}$$

Least common multiple of 1100 and 176 is 4400. Convert \frac{81}{1100} and \frac{1}{176} to fractions with denominator 4400.

$$\left(\frac{324}{4400}+\frac{25}{4400}\right)\times \frac{30^{2}}{4}$$

Since \frac{324}{4400} and \frac{25}{4400} have the same denominator, add them by adding their numerators.

$$\frac{324+25}{4400}\times \frac{30^{2}}{4}$$

Add 324 and 25 to get 349.

$$\frac{349}{4400}\times \frac{30^{2}}{4}$$

Calculate 30 to the power of 2 and get 900.

$$\frac{349}{4400}\times \frac{900}{4}$$

Divide 900 by 4 to get 225.

$$\frac{349}{4400}\times 225$$

Express \frac{349}{4400}\times 225 as a single fraction.

$$\frac{349\times 225}{4400}$$

Multiply 349 and 225 to get 78525.

$$\frac{78525}{4400}$$

Reduce the fraction \frac{78525}{4400} to lowest terms by extracting and canceling out 25.

$$\frac{3141}{176}$$

Factor

$$\frac{349 \cdot 3 ^ {2}}{11 \cdot 2 ^ {4}} = 17\frac{149}{176} = 17.84659090909091$$