Solve 30+72.222[1-0.2*8/13-0.8*8/13)^2]=

$$30 + 72.222 [ 1 - 0.2 \times \frac { 8 } { 13 } - 0.8 \times \frac { 8 } { 13 } ) ^ { 2 } ] =$$

Evaluate

$$\frac{137511}{3380}\approx 40.683727811$$

Solution Steps

Multiply 0.2 and \frac{8}{13} to get \frac{8}{65}.

$$30+72.222\left(1-\frac{8}{65}-0.8\times \frac{8}{13}\right)^{2}$$

Subtract \frac{8}{65} from 1 to get \frac{57}{65}.

$$30+72.222\left(\frac{57}{65}-0.8\times \frac{8}{13}\right)^{2}$$

Multiply 0.8 and \frac{8}{13} to get \frac{32}{65}.

$$30+72.222\left(\frac{57}{65}-\frac{32}{65}\right)^{2}$$

Subtract \frac{32}{65} from \frac{57}{65} to get \frac{5}{13}.

$$30+72.222\times \left(\frac{5}{13}\right)^{2}$$

Calculate \frac{5}{13} to the power of 2 and get \frac{25}{169}.

$$30+72.222\times \frac{25}{169}$$

Multiply 72.222 and \frac{25}{169} to get \frac{36111}{3380}.

$$30+\frac{36111}{3380}$$

Add 30 and \frac{36111}{3380} to get \frac{137511}{3380}.

$$\frac{137511}{3380}$$

Factor

$$\frac{11 \cdot 463 \cdot 3 ^ {3}}{5 \cdot 2 ^ {2} \cdot 13 ^ {2}} = 40\frac{2311}{3380} = 40.683727810650886$$