Solve by Completing the Square 3x^2+18x+6=0

$3 x^{2} + 18 x + 6 = 0$

Step 1

Subtract $6$ from both sides of the equation.

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

Step 2

Divide each term in $3 x^{2} + 18 x = - 6$ by $3$ and simplify.

Divide each term in $3 x^{2} + 18 x = - 6$ by $3$ .

$\frac{3 x^{2}}{3} + \frac{18 x}{3} = \frac{- 6}{3}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} + \frac{18 x}{3} = \frac{- 6}{3}$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{18 x}{3} = \frac{- 6}{3}$

Cancel the common factor of $18$ and $3$ .

Factor $3$ out of $18 x$ .

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

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{2} + \frac{3 (6 x)}{3 (1)} = \frac{- 6}{3}$

Cancel the common factor.

$x^{2} + \frac{3 (6 x)}{3 \cdot 1} = \frac{- 6}{3}$

Rewrite the expression.

$x^{2} + \frac{6 x}{1} = \frac{- 6}{3}$

Divide $6 x$ by $1$ .

$x^{2} + 6 x = \frac{- 6}{3}$

Simplify the right side.

Divide $- 6$ by $3$ .

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

Step 3

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 4

Add the term to each side of the equation.

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

Step 5

Simplify the equation.

Simplify the left side.

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

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

Simplify the right side.

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

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

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

Add $- 2$ and $9$ .

$x^{2} + 6 x + 9 = 7$

Step 6

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

${(x + 3)}^{2} = 7$

Step 7

Solve the equation for $x$ .

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

$x + 3 = \pm \sqrt{7}$

Subtract $3$ from both sides of the equation.

$x = \pm \sqrt{7} - 3$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{7} - 3$

Decimal Form:

$x = - 0.35424868 \dots, - 5.64575131 \dots$

Solve by Completing the Square 3x^2+18x+6=0

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