Solve 2+2(-frac{sqrt{2}}{4}-1/2)

$$2 + 2 ( - \frac { \sqrt { 2 } } { 4 } - \frac { 1 } { 2 } )$$

Evaluate

$$-\frac{\sqrt{2}}{2}+1\approx 0.292893219$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4 and 2 is 4. Multiply \frac{1}{2} times \frac{2}{2}.

$$2+2\left(-\frac{\sqrt{2}}{4}-\frac{2}{4}\right)$$

Since -\frac{\sqrt{2}}{4} and \frac{2}{4} have the same denominator, subtract them by subtracting their numerators.

$$2+2\times \frac{-\sqrt{2}-2}{4}$$

Cancel out 4, the greatest common factor in 2 and 4.

$$2+\frac{-\sqrt{2}-2}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{2}{2}.

$$\frac{2\times 2}{2}+\frac{-\sqrt{2}-2}{2}$$

Since \frac{2\times 2}{2} and \frac{-\sqrt{2}-2}{2} have the same denominator, add them by adding their numerators.

$$\frac{2\times 2-\sqrt{2}-2}{2}$$

Do the multiplications in 2\times 2-\sqrt{2}-2.

$$\frac{4-\sqrt{2}-2}{2}$$

Do the calculations in 4-\sqrt{2}-2.

$$\frac{2-\sqrt{2}}{2}$$

Factor

$$\frac{\sqrt{2} {(\sqrt{2} - 1)}}{2} = 0.29289321881345254$$