Solve by Completing the Square x^2+6x=-14

$x^{2} + 6 x = - 14$

Step 1

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(3)}^{2}$

Step 2

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = - 14 + {(3)}^{2}$

Step 3

Simplify the equation.

Simplify the left side.

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = - 14 + {(3)}^{2}$

Simplify the right side.

Simplify $- 14 + {(3)}^{2}$ .

Raise $3$ to the power of $2$ .

$x^{2} + 6 x + 9 = - 14 + 9$

Add $- 14$ and $9$ .

$x^{2} + 6 x + 9 = - 5$

Step 4

Factor the perfect trinomial square into ${(x + 3)}^{2}$ .

${(x + 3)}^{2} = - 5$

Step 5

Solve the equation for $x$ .

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

$x + 3 = \pm \sqrt{- 5}$

Simplify $\pm \sqrt{- 5}$ .

Rewrite $- 5$ as $- 1 (5)$ .

$x + 3 = \pm \sqrt{- 1 (5)}$

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$x + 3 = \pm \sqrt{- 1} \cdot \sqrt{5}$

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

$x + 3 = \pm i \sqrt{5}$

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

Subtract $3$ from both sides of the equation.

$x = \pm i \sqrt{5} - 3$

Reorder $\pm i \sqrt{5}$ and $- 3$ .

$x = - 3 \pm i \sqrt{5}$