Algebra Examples

${(x + 3)}^{2} = - 16$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x + 3 = \pm \sqrt{- 16}$

Step 2

Simplify $\pm \sqrt{- 16}$ .

Tap for more steps...

Step 2.1

Rewrite $- 16$ as $- 1 (16)$ .

$x + 3 = \pm \sqrt{- 1 (16)}$

Step 2.2

Rewrite $\sqrt{- 1 (16)}$ as $\sqrt{- 1} \cdot \sqrt{16}$ .

$x + 3 = \pm \sqrt{- 1} \cdot \sqrt{16}$

Step 2.3

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

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

Step 2.4

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

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

Step 2.5

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

$x + 3 = \pm i \cdot 4$

Step 2.6

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

$x + 3 = \pm 4 i$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 3.1

First, use the positive value of the $\pm$ to find the first solution.

$x + 3 = 4 i$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Subtract $3$ from both sides of the equation.

$x = 4 i - 3$

Step 3.2.2

Reorder $4 i$ and $- 3$ .

$x = - 3 + 4 i$

Step 3.3

Next, use the negative value of the $\pm$ to find the second solution.

$x + 3 = - 4 i$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Subtract $3$ from both sides of the equation.

$x = - 4 i - 3$

Step 3.4.2

Reorder $- 4 i$ and $- 3$ .

$x = - 3 - 4 i$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

$x = - 3 + 4 i, - 3 - 4 i$