Solve ((11-137)^2/137)+[(41-38*3)^2/38*3]+[(48-15*3)^2/15*3]+[(40-42*7)^2/42*7]

$$( \frac { ( 11 - 137 ) ^ { 2 } } { 137 } ) + [ \frac { ( 41 - 38 \cdot 3 ) ^ { 2 } } { 38 \cdot 3 } ] + [ \frac { ( 48 - 15 \cdot 3 ) ^ { 2 } } { 15 \cdot 3 } ] + [ \frac { ( 40 - 42 \cdot 7 ) ^ { 2 } } { 42 \cdot 7 } ]$$

Evaluate

$$\frac{1462725587}{3826410}\approx 382.271002585$$

Solution Steps

Subtract 137 from 11 to get -126.

$$\frac{\left(-126\right)^{2}}{137}+\frac{\left(41-38\times 3\right)^{2}}{38\times 3}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Calculate -126 to the power of 2 and get 15876.

$$\frac{15876}{137}+\frac{\left(41-38\times 3\right)^{2}}{38\times 3}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Multiply 38 and 3 to get 114.

$$\frac{15876}{137}+\frac{\left(41-114\right)^{2}}{38\times 3}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Subtract 114 from 41 to get -73.

$$\frac{15876}{137}+\frac{\left(-73\right)^{2}}{38\times 3}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Calculate -73 to the power of 2 and get 5329.

$$\frac{15876}{137}+\frac{5329}{38\times 3}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Multiply 38 and 3 to get 114.

$$\frac{15876}{137}+\frac{5329}{114}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Add \frac{15876}{137} and \frac{5329}{114} to get \frac{2539937}{15618}.

$$\frac{2539937}{15618}+\frac{\left(48-15\times 3\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Multiply 15 and 3 to get 45.

$$\frac{2539937}{15618}+\frac{\left(48-45\right)^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Subtract 45 from 48 to get 3.

$$\frac{2539937}{15618}+\frac{3^{2}}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2539937}{15618}+\frac{9}{15\times 3}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Multiply 15 and 3 to get 45.

$$\frac{2539937}{15618}+\frac{9}{45}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Reduce the fraction \frac{9}{45} to lowest terms by extracting and canceling out 9.

$$\frac{2539937}{15618}+\frac{1}{5}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Add \frac{2539937}{15618} and \frac{1}{5} to get \frac{12715303}{78090}.

$$\frac{12715303}{78090}+\frac{\left(40-42\times 7\right)^{2}}{42\times 7}$$

Multiply 42 and 7 to get 294.

$$\frac{12715303}{78090}+\frac{\left(40-294\right)^{2}}{42\times 7}$$

Subtract 294 from 40 to get -254.

$$\frac{12715303}{78090}+\frac{\left(-254\right)^{2}}{42\times 7}$$

Calculate -254 to the power of 2 and get 64516.

$$\frac{12715303}{78090}+\frac{64516}{42\times 7}$$

Multiply 42 and 7 to get 294.

$$\frac{12715303}{78090}+\frac{64516}{294}$$

Reduce the fraction \frac{64516}{294} to lowest terms by extracting and canceling out 2.

$$\frac{12715303}{78090}+\frac{32258}{147}$$

Add \frac{12715303}{78090} and \frac{32258}{147} to get \frac{1462725587}{3826410}.

$$\frac{1462725587}{3826410}$$

Factor

$$\frac{47 \cdot 31121821}{2 \cdot 3 \cdot 5 \cdot 7 ^ {2} \cdot 19 \cdot 137} = 382\frac{1036967}{3826410} = 382.2710025846681$$