Solve Using the Quadratic Formula 3x^2+12x+1=0

$3 x^{2} + 12 x + 1 = 0$

Step 1

Use the quadratic formula to find the solutions.

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

Step 2

Substitute the values $a = 3$ , $b = 12$ , and $c = 1$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (3 \cdot 1)}}{2 \cdot 3}$

Step 3

Simplify.

Simplify the numerator.

Raise $12$ to the power of $2$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 3 \cdot 1}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 1$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 12 \pm \sqrt{144 - 12 \cdot 1}}{2 \cdot 3}$

Multiply $- 12$ by $1$ .

$x = \frac{- 12 \pm \sqrt{144 - 12}}{2 \cdot 3}$

Subtract $12$ from $144$ .

$x = \frac{- 12 \pm \sqrt{132}}{2 \cdot 3}$

Rewrite $132$ as $2^{2} \cdot 33$ .

Factor $4$ out of $132$ .

$x = \frac{- 12 \pm \sqrt{4 (33)}}{2 \cdot 3}$

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

$x = \frac{- 12 \pm \sqrt{2^{2} \cdot 33}}{2 \cdot 3}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 2 \sqrt{33}}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 12 \pm 2 \sqrt{33}}{6}$

Simplify $\frac{- 12 \pm 2 \sqrt{33}}{6}$ .

$x = \frac{- 6 \pm \sqrt{33}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{- 6 \pm \sqrt{33}}{3}$

Decimal Form:

$x = - 0.08514578 \dots, - 3.91485421 \dots$