Solve for x 2x^2-12x=-6

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

Add $6$ to both sides of the equation.

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

Factor $2$ out of $2 x^{2} - 12 x + 6$ .

Factor $2$ out of $2 x^{2}$ .

$2 (x^{2}) - 12 x + 6 = 0$

Factor $2$ out of $- 12 x$ .

$2 (x^{2}) + 2 (- 6 x) + 6 = 0$

Factor $2$ out of $6$ .

$2 x^{2} + 2 (- 6 x) + 2 \cdot 3 = 0$

Factor $2$ out of $2 x^{2} + 2 (- 6 x)$ .

$2 (x^{2} - 6 x) + 2 \cdot 3 = 0$

Factor $2$ out of $2 (x^{2} - 6 x) + 2 \cdot 3$ .

$2 (x^{2} - 6 x + 3) = 0$

Divide each term in $2 (x^{2} - 6 x + 3) = 0$ by $2$ and simplify.

Divide each term in $2 (x^{2} - 6 x + 3) = 0$ by $2$ .

$\frac{2 (x^{2} - 6 x + 3)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 (x^{2} - 6 x + 3)}{2} = \frac{0}{2}$

Divide $x^{2} - 6 x + 3$ by $1$ .

$x^{2} - 6 x + 3 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

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

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Substitute the values $a = 1$ , $b = - 6$ , and $c = 3$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 3)}}{2 \cdot 1}$

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 3}}{2 \cdot 1}$

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 3}}{2 \cdot 1}$

Multiply $- 4$ by $3$ .

$x = \frac{6 \pm \sqrt{36 - 12}}{2 \cdot 1}$

Subtract $12$ from $36$ .

$x = \frac{6 \pm \sqrt{24}}{2 \cdot 1}$

Rewrite $24$ as $2^{2} \cdot 6$ .

Factor $4$ out of $24$ .

$x = \frac{6 \pm \sqrt{4 (6)}}{2 \cdot 1}$

Rewrite $4$ as $2^{2}$ .

$x = \frac{6 \pm \sqrt{2^{2} \cdot 6}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{6 \pm 2 \sqrt{6}}{2 \cdot 1}$

Multiply $2$ by $1$ .

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

Simplify $\frac{6 \pm 2 \sqrt{6}}{2}$ .

$x = 3 \pm \sqrt{6}$

The final answer is the combination of both solutions.

$x = 3 + \sqrt{6}, 3 - \sqrt{6}$

The result can be shown in multiple forms.

Exact Form:

$x = 3 + \sqrt{6}, 3 - \sqrt{6}$

Decimal Form:

$x = 5.44948974 \dots, 0.55051025 \dots$

Solve for x 2x^2-12x=-6

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