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

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

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.

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

Step 3

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

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

Add $18$ and $9$ .

$x^{2} + 6 x + 9 = 27$

Step 4

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

${(x + 3)}^{2} = 27$

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.

$x + 3 = \pm \sqrt{27}$

Simplify $\pm \sqrt{27}$ .

Rewrite $27$ as $3^{2} \cdot 3$ .

Factor $9$ out of $27$ .

$x + 3 = \pm \sqrt{9 (3)}$

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

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

Pull terms out from under the radical.

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

Subtract $3$ from both sides of the equation.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.19615242 \dots, - 8.19615242 \dots$