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

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

Evaluate

$$-\frac{\sqrt{2}}{2}-1\approx -1.707106781$$

Short Solution Steps

The square of \sqrt{3} is 3.

$$-\frac{\sqrt{2}}{2}-3+4\times \frac{1}{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 3 times \frac{2}{2}.

$$-\frac{\sqrt{2}}{2}-\frac{3\times 2}{2}+4\times \frac{1}{2}$$

Since -\frac{\sqrt{2}}{2} and \frac{3\times 2}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-\sqrt{2}-3\times 2}{2}+4\times \frac{1}{2}$$

Do the multiplications in -\sqrt{2}-3\times 2.

$$\frac{-\sqrt{2}-6}{2}+4\times \frac{1}{2}$$

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

$$\frac{-\sqrt{2}-6}{2}+2$$

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

$$\frac{-\sqrt{2}-6}{2}+\frac{2\times 2}{2}$$

Since \frac{-\sqrt{2}-6}{2} and \frac{2\times 2}{2} have the same denominator, add them by adding their numerators.

$$\frac{-\sqrt{2}-6+2\times 2}{2}$$

Do the multiplications in -\sqrt{2}-6+2\times 2.

$$\frac{-\sqrt{2}-6+4}{2}$$

Do the calculations in -\sqrt{2}-6+4.

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

Factor

$$\frac{-\sqrt{2} - 2}{2} = -1.7071067811865475$$