Solve by Completing the Square x^2+6x+18=0

$x^{2} + 6 x + 18 = 0$

Subtract $18$ from both sides of the equation.

$x^{2} + 6 x = - 18$

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

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

Add the term to each side of the equation.

$x^{2} + 6 x + {(3)}^{2} = - 18 + {(3)}^{2}$

Simplify the equation.

Tap for more steps…

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

$x^{2} + 6 x + 9 = - 18 + {(3)}^{2}$

Simplify $- 18 + {(3)}^{2}$ .

Tap for more steps…

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

$x^{2} + 6 x + 9 = - 18 + 9$

Add $- 18$ and $9$ .

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

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

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

Solve the equation for $x$ .

Tap for more steps…

Take the square root of each side of the equation to set up the solution for $x$

${(x + 3)}^{2 \cdot \frac{1}{2}} = \pm \sqrt{- 9}$

Remove the perfect root factor $x + 3$ under the radical to solve for $x$ .

$x + 3 = \pm \sqrt{- 9}$

Simplify the right side of the equation.

Tap for more steps…

Rewrite $- 9$ as $- 1 (9)$ .

$x + 3 = \pm \sqrt{- 1 \cdot 9}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$x + 3 = \pm \sqrt{- 1} \cdot \sqrt{9}$

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

$x + 3 = \pm i \cdot \sqrt{9}$

Rewrite $9$ as $3^{2}$ .

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

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

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

Move $3$ to the left of $i$ .

$x + 3 = \pm 3 i$

Remove parentheses.

$x + 3 = \pm 3 i$

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

Tap for more steps…

Subtract $3$ from both sides of the equation.

$x = \pm 3 i - 3$

Reorder $\pm 3 i$ and $- 3$ .

$x = - 3 \pm 3 i$

Solve by Completing the Square x^2+6x+18=0

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Download our
App from the store