Solve 0.828+0.2div2left(0.828+0.2right)^2+1

$$0.828+0.2 \div 2 { \left(0.828+0.2 \right) }^{ 2 } +1$$

Evaluate

$$1.9336784$$

Solution Steps

Expand \frac{0.2}{2} by multiplying both numerator and the denominator by 10.

$$0.828+\frac{2}{20}\left(0.828+0.2\right)^{2}+1$$

Reduce the fraction \frac{2}{20} to lowest terms by extracting and canceling out 2.

$$0.828+\frac{1}{10}\left(0.828+0.2\right)^{2}+1$$

Add 0.828 and 0.2 to get 1.028.

$$0.828+\frac{1}{10}\times 1.028^{2}+1$$

Calculate 1.028 to the power of 2 and get 1.056784.

$$0.828+\frac{1}{10}\times 1.056784+1$$

Multiply \frac{1}{10} and 1.056784 to get \frac{66049}{625000}.

$$0.828+\frac{66049}{625000}+1$$

Add 0.828 and \frac{66049}{625000} to get \frac{583549}{625000}.

$$\frac{583549}{625000}+1$$

Add \frac{583549}{625000} and 1 to get \frac{1208549}{625000}.

$$\frac{1208549}{625000}$$

Factor

$$\frac{977 \cdot 1237}{2 ^ {3} \cdot 5 ^ {7}} = 1\frac{583549}{625000} = 1.9336784$$