Algebra Examples

$x = 3 + \sqrt{- 48}$

Step 1

Move all terms to the left side of the equation and simplify.

Tap for more steps...

Step 1.1

Simplify the right side.

Tap for more steps...

Step 1.1.1

Simplify each term.

Tap for more steps...

Step 1.1.1.1

Rewrite $- 48$ as $- 1 (48)$ .

$x = 3 + \sqrt{- 1 (48)}$

Step 1.1.1.2

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$x = 3 + \sqrt{- 1} \cdot \sqrt{48}$

Step 1.1.1.3

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

$x = 3 + i \cdot \sqrt{48}$

Step 1.1.1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

Tap for more steps...

Step 1.1.1.4.1

Factor $16$ out of $48$ .

$x = 3 + i \cdot \sqrt{16 (3)}$

Step 1.1.1.4.2

Rewrite $16$ as $4^{2}$ .

$x = 3 + i \cdot \sqrt{4^{2} \cdot 3}$

Step 1.1.1.5

Pull terms out from under the radical.

$x = 3 + i \cdot (4 \sqrt{3})$

Step 1.1.1.6

Move $4$ to the left of $i$ .

$x = 3 + 4 i \sqrt{3}$

Step 1.2

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.2.1

Subtract $3$ from both sides of the equation.

$x - 3 = 4 i \sqrt{3}$

Step 1.2.2

Subtract $4 i \sqrt{3}$ from both sides of the equation.

$x - 3 - 4 i \sqrt{3} = 0$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Tap for more steps...

Step 2.1

Add $3$ to both sides of the equation.

$x - 4 i \sqrt{3} = 3$

Step 2.2

Add $4 i \sqrt{3}$ to both sides of the equation.

$x = 3 + 4 i \sqrt{3}$