Precalculus Examples

$\frac{1}{2} \cdot (- 7 + \sqrt{413})$

Step 1

Apply the distributive property.

$\frac{1}{2} \cdot - 7 + \frac{1}{2} \sqrt{413}$

Step 2

Combine $\frac{1}{2}$ and $- 7$ .

$\frac{- 7}{2} + \frac{1}{2} \sqrt{413}$

Step 3

Combine $\frac{1}{2}$ and $\sqrt{413}$ .

$\frac{- 7}{2} + \frac{\sqrt{413}}{2}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 7 + \sqrt{413}}{2}$

Step 5

Rewrite $- 7$ as $- 1 (7)$ .

$\frac{- 1 (7) + \sqrt{413}}{2}$

Step 6

Factor $- 1$ out of $\sqrt{413}$ .

$\frac{- 1 (7) - 1 (- \sqrt{413})}{2}$

Step 7

Factor $- 1$ out of $- 1 (7) - 1 (- \sqrt{413})$ .

$\frac{- 1 (7 - \sqrt{413})}{2}$

Step 8

Move the negative in front of the fraction.

$- \frac{7 - \sqrt{413}}{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{7 - \sqrt{413}}{2}$

Decimal Form:

$6.66120071 \dots$