Solve {left(1/2+5right)}^2*1/2+2*{left(1/2right)}^2-{left(1/2right)}^3+3*frac{1}{2}-18

$${ \left( \frac{ 1 }{ 2 } +5 \right) }^{ 2 } \times \frac{ 1 }{ 2 } +2 \times { \left( \frac{ 1 }{ 2 } \right) }^{ 2 } - { \left( \frac{ 1 }{ 2 } \right) }^{ 3 } +3 \times \frac{ 1 }{ 2 } -18$$

Evaluate

$$-1$$

Solution Steps

Add \frac{1}{2} and 5 to get \frac{11}{2}.

$$\left(\frac{11}{2}\right)^{2}\times \frac{1}{2}+2\times \left(\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Calculate \frac{11}{2} to the power of 2 and get \frac{121}{4}.

$$\frac{121}{4}\times \frac{1}{2}+2\times \left(\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Multiply \frac{121}{4} and \frac{1}{2} to get \frac{121}{8}.

$$\frac{121}{8}+2\times \left(\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Calculate \frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$\frac{121}{8}+2\times \frac{1}{4}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$\frac{121}{8}+\frac{1}{2}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Add \frac{121}{8} and \frac{1}{2} to get \frac{125}{8}.

$$\frac{125}{8}-\left(\frac{1}{2}\right)^{3}+3\times \frac{1}{2}-18$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\frac{125}{8}-\frac{1}{8}+3\times \frac{1}{2}-18$$

Subtract \frac{1}{8} from \frac{125}{8} to get \frac{31}{2}.

$$\frac{31}{2}+3\times \frac{1}{2}-18$$

Multiply 3 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{31}{2}+\frac{3}{2}-18$$

Add \frac{31}{2} and \frac{3}{2} to get 17.

$$17-18$$

Subtract 18 from 17 to get -1.

$$-1$$

Factor

$$-1$$