Solve sum(frac{sqrt{2}}{2})+5sqrt{2}(-1)

$$\sum ( \frac { \sqrt { 2 } } { 2 } ) + 5 \sqrt { 2 } ( - 1 )$$

Evaluate

$$\frac{\sqrt{2}\left(Σ-10\right)}{2}$$

Short Solution Steps

Express Σ\times \frac{\sqrt{2}}{2} as a single fraction.

$$\frac{Σ\sqrt{2}}{2}+5\sqrt{2}\left(-1\right)$$

Multiply 5 and -1 to get -5.

$$\frac{Σ\sqrt{2}}{2}-5\sqrt{2}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -5\sqrt{2} times \frac{2}{2}.

$$\frac{Σ\sqrt{2}}{2}+\frac{2\left(-5\right)\sqrt{2}}{2}$$

Since \frac{Σ\sqrt{2}}{2} and \frac{2\left(-5\right)\sqrt{2}}{2} have the same denominator, add them by adding their numerators.

$$\frac{Σ\sqrt{2}+2\left(-5\right)\sqrt{2}}{2}$$

Do the multiplications in Σ\sqrt{2}+2\left(-5\right)\sqrt{2}.

$$\frac{Σ\sqrt{2}-10\sqrt{2}}{2}$$

Factor

$$\frac{\sqrt{2}\left(Σ-10\right)}{2}$$

Solution Steps

Factor out \frac{1}{2}.

$$\frac{Σ\sqrt{2}-10\sqrt{2}}{2}$$

Consider Σ\sqrt{2}-10\sqrt{2}. Factor out \sqrt{2}.

$$\sqrt{2}\left(Σ-10\right)$$

Rewrite the complete factored expression.

$$\frac{\sqrt{2}\left(Σ-10\right)}{2}$$