Solve -{[-(-1+1/2)^{2}+1/3]^2-[(-1+1/2)^4-(-1/3+frac{1}{2})^2]}-(-frac{1}{2}+1)+(-frac{1}{2})^2

$$- \{ [ - ( - 1 + \frac { 1 } { 2 } ) ^ { 2 } + \frac { 1 } { 3 } ] ^ { 2 } - [ ( - 1 + \frac { 1 } { 2 } ) ^ { 4 } - ( - \frac { 1 } { 3 } + \frac { 1 } { 2 } ) ^ { 2 } ] \} - ( - \frac { 1 } { 2 } + 1 ) + ( - \frac { 1 } { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{2}{9}\approx -0.222222222$$

Solution Steps

Add -1 and \frac{1}{2} to get -\frac{1}{2}.

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

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

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

Add -\frac{1}{4} and \frac{1}{3} to get \frac{1}{12}.

$$-\left(\left(\frac{1}{12}\right)^{2}-\left(\left(-1+\frac{1}{2}\right)^{4}-\left(-\frac{1}{3}+\frac{1}{2}\right)^{2}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{12} to the power of 2 and get \frac{1}{144}.

$$-\left(\frac{1}{144}-\left(\left(-1+\frac{1}{2}\right)^{4}-\left(-\frac{1}{3}+\frac{1}{2}\right)^{2}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Add -1 and \frac{1}{2} to get -\frac{1}{2}.

$$-\left(\frac{1}{144}-\left(\left(-\frac{1}{2}\right)^{4}-\left(-\frac{1}{3}+\frac{1}{2}\right)^{2}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$-\left(\frac{1}{144}-\left(\frac{1}{16}-\left(-\frac{1}{3}+\frac{1}{2}\right)^{2}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Add -\frac{1}{3} and \frac{1}{2} to get \frac{1}{6}.

$$-\left(\frac{1}{144}-\left(\frac{1}{16}-\left(\frac{1}{6}\right)^{2}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$-\left(\frac{1}{144}-\left(\frac{1}{16}-\frac{1}{36}\right)\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Subtract \frac{1}{36} from \frac{1}{16} to get \frac{5}{144}.

$$-\left(\frac{1}{144}-\frac{5}{144}\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Subtract \frac{5}{144} from \frac{1}{144} to get -\frac{1}{36}.

$$-\left(-\frac{1}{36}\right)-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

The opposite of -\frac{1}{36} is \frac{1}{36}.

$$\frac{1}{36}-\left(-\frac{1}{2}+1\right)+\left(-\frac{1}{2}\right)^{2}$$

Add -\frac{1}{2} and 1 to get \frac{1}{2}.

$$\frac{1}{36}-\frac{1}{2}+\left(-\frac{1}{2}\right)^{2}$$

Subtract \frac{1}{2} from \frac{1}{36} to get -\frac{17}{36}.

$$-\frac{17}{36}+\left(-\frac{1}{2}\right)^{2}$$

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

$$-\frac{17}{36}+\frac{1}{4}$$

Add -\frac{17}{36} and \frac{1}{4} to get -\frac{2}{9}.

$$-\frac{2}{9}$$

Factor

$$-\frac{2}{9} = -0.2222222222222222$$