Solve by Completing the Square x^2+6x+9=0

$x^{2} + 6 x + 9 = 0$

Step 1

Subtract $9$ from both sides of the equation.

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

Step 2

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 3

Add the term to each side of the equation.

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

Step 4

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

Simplify $- 9 + {(3)}^{2}$ .

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

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

Add $- 9$ and $9$ .

$x^{2} + 6 x + 9 = 0$

Step 5

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

${(x + 3)}^{2} = 0$

Step 6

Solve the equation for $x$ .

Set the $x + 3$ equal to $0$ .

$x + 3 = 0$

Subtract $3$ from both sides of the equation.

$x = - 3$