Solve Using the Quadratic Formula x^2+12x+33=0

$x^{2} + 12 x + 33 = 0$

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 $a = 1$ , $b = 12$ , and $c = 33$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (1 \cdot 33)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 1 \cdot 33}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 33$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 33}}{2 \cdot 1}$

Multiply $- 4$ by $33$ .

$x = \frac{- 12 \pm \sqrt{144 - 132}}{2 \cdot 1}$

Subtract $132$ from $144$ .

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

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $1$ .

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

Simplify $\frac{- 12 \pm 2 \sqrt{3}}{2}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 4.26794919 \dots, - 7.73205080 \dots$