Solve for x x=(5+ square root of -49)/6

$x = \frac{5 + \sqrt{- 49}}{6}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 49$ as $- 1 (49)$ .

$x = \frac{5 + \sqrt{- 1 (49)}}{6}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$x = \frac{5 + \sqrt{- 1} \cdot \sqrt{49}}{6}$

Rewrite $\sqrt{- 1}$ as $i$ .

$x = \frac{5 + i \cdot \sqrt{49}}{6}$

Step 2

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$x = \frac{5 + i \cdot \sqrt{7^{2}}}{6}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{5 + i \cdot 7}{6}$

Move $7$ to the left of $i$ .

$x = \frac{5 + 7 i}{6}$

Step 3

Split the fraction $\frac{5 + 7 i}{6}$ into two fractions.

$x = \frac{5}{6} + \frac{7 i}{6}$