Solve (-50-32.4)^2*0.28+(20-32.4)^2*0.32+(100-32.4)^2*0.4

$$( - 50 - 32.4 ) ^ { 2 } \times 0.28 + ( 20 - 32.4 ) ^ { 2 } \times 0.32 + ( 100 - 32.4 ) ^ { 2 } \times 0.4$$

Evaluate

$$3778.24$$

Solution Steps

Subtract 32.4 from -50 to get -82.4.

$$\left(-82.4\right)^{2}\times 0.28+\left(20-32.4\right)^{2}\times 0.32+\left(100-32.4\right)^{2}\times 0.4$$

Calculate -82.4 to the power of 2 and get 6789.76.

$$6789.76\times 0.28+\left(20-32.4\right)^{2}\times 0.32+\left(100-32.4\right)^{2}\times 0.4$$

Multiply 6789.76 and 0.28 to get 1901.1328.

$$1901.1328+\left(20-32.4\right)^{2}\times 0.32+\left(100-32.4\right)^{2}\times 0.4$$

Subtract 32.4 from 20 to get -12.4.

$$1901.1328+\left(-12.4\right)^{2}\times 0.32+\left(100-32.4\right)^{2}\times 0.4$$

Calculate -12.4 to the power of 2 and get 153.76.

$$1901.1328+153.76\times 0.32+\left(100-32.4\right)^{2}\times 0.4$$

Multiply 153.76 and 0.32 to get 49.2032.

$$1901.1328+49.2032+\left(100-32.4\right)^{2}\times 0.4$$

Add 1901.1328 and 49.2032 to get 1950.336.

$$1950.336+\left(100-32.4\right)^{2}\times 0.4$$

Subtract 32.4 from 100 to get 67.6.

$$1950.336+67.6^{2}\times 0.4$$

Calculate 67.6 to the power of 2 and get 4569.76.

$$1950.336+4569.76\times 0.4$$

Multiply 4569.76 and 0.4 to get 1827.904.

$$1950.336+1827.904$$

Add 1950.336 and 1827.904 to get 3778.24.

$$3778.24$$

Factor

$$\frac{11807 \cdot 2 ^ {3}}{5 ^ {2}} = 3778\frac{6}{25} = 3778.24$$