Solve by Completing the Square 3x^2-12x-6=0

$3 x^{2} - 12 x - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$3 x^{2} - 12 x = 6$

Step 2

Divide each term in $3 x^{2} - 12 x = 6$ by $3$ and simplify.

Divide each term in $3 x^{2} - 12 x = 6$ by $3$ .

$\frac{3 x^{2}}{3} + \frac{- 12 x}{3} = \frac{6}{3}$

Simplify the left side.

Simplify each term.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x^{2}}{3} + \frac{- 12 x}{3} = \frac{6}{3}$

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

$x^{2} + \frac{- 12 x}{3} = \frac{6}{3}$

Cancel the common factor of $- 12$ and $3$ .

Factor $3$ out of $- 12 x$ .

$x^{2} + \frac{3 (- 4 x)}{3} = \frac{6}{3}$

Cancel the common factors.

Factor $3$ out of $3$ .

$x^{2} + \frac{3 (- 4 x)}{3 (1)} = \frac{6}{3}$

Cancel the common factor.

$x^{2} + \frac{3 (- 4 x)}{3 \cdot 1} = \frac{6}{3}$

Rewrite the expression.

$x^{2} + \frac{- 4 x}{1} = \frac{6}{3}$

Divide $- 4 x$ by $1$ .

$x^{2} - 4 x = \frac{6}{3}$

Simplify the right side.

Divide $6$ by $3$ .

$x^{2} - 4 x = 2$

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 $b$ .

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

Step 4

Add the term to each side of the equation.

$x^{2} - 4 x + {(- 2)}^{2} = 2 + {(- 2)}^{2}$

Step 5

Simplify the equation.

Simplify the left side.

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

$x^{2} - 4 x + 4 = 2 + {(- 2)}^{2}$

Simplify the right side.

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

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

$x^{2} - 4 x + 4 = 2 + 4$

Add $2$ and $4$ .

$x^{2} - 4 x + 4 = 6$

Step 6

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

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

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.

$x - 2 = \pm \sqrt{6}$

Add $2$ to both sides of the equation.

$x = \pm \sqrt{6} + 2$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{6} + 2$

Decimal Form:

$x = 4.44948974 \dots, - 0.44948974 \dots$

Solve by Completing the Square 3x^2-12x-6=0

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