Solve 36.36*(3.78-0.9)^2+40.91*(0.26-0.9)^2+22.73*(2.57+0.9)^2

$$36.36 \times ( 3.78 - 0.9 ) ^ { 2 } + 40.91 \times ( 0.26 - 0.9 ) ^ { 2 } + 22.73 \times ( 2.57 + 0.9 ) ^ { 2 }$$

Evaluate

$$592.030777$$

Solution Steps

Subtract 0.9 from 3.78 to get 2.88.

$$36.36\times 2.88^{2}+40.91\left(0.26-0.9\right)^{2}+22.73\left(2.57+0.9\right)^{2}$$

Calculate 2.88 to the power of 2 and get 8.2944.

$$36.36\times 8.2944+40.91\left(0.26-0.9\right)^{2}+22.73\left(2.57+0.9\right)^{2}$$

Multiply 36.36 and 8.2944 to get 301.584384.

$$301.584384+40.91\left(0.26-0.9\right)^{2}+22.73\left(2.57+0.9\right)^{2}$$

Subtract 0.9 from 0.26 to get -0.64.

$$301.584384+40.91\left(-0.64\right)^{2}+22.73\left(2.57+0.9\right)^{2}$$

Calculate -0.64 to the power of 2 and get 0.4096.

$$301.584384+40.91\times 0.4096+22.73\left(2.57+0.9\right)^{2}$$

Multiply 40.91 and 0.4096 to get 16.756736.

$$301.584384+16.756736+22.73\left(2.57+0.9\right)^{2}$$

Add 301.584384 and 16.756736 to get 318.34112.

$$318.34112+22.73\left(2.57+0.9\right)^{2}$$

Add 2.57 and 0.9 to get 3.47.

$$318.34112+22.73\times 3.47^{2}$$

Calculate 3.47 to the power of 2 and get 12.0409.

$$318.34112+22.73\times 12.0409$$

Multiply 22.73 and 12.0409 to get 273.689657.

$$318.34112+273.689657$$

Add 318.34112 and 273.689657 to get 592.030777.

$$592.030777$$

Factor

$$\frac{13 \cdot 47389 \cdot 31 ^ {2}}{2 ^ {6} \cdot 5 ^ {6}} = 592\frac{30777}{1000000} = 592.030777$$