Solve Using the Quadratic Formula x^2+12x-9=0

$x^{2} + 12 x - 9 = 0$

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 $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{- 12 \pm \sqrt{12^{2} - 4 \cdot (1 \cdot - 9)}}{2 \cdot 1}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot 1 \cdot - 9}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 9$ .

Multiply $- 4$ by $1$ .

$x = \frac{- 12 \pm \sqrt{144 - 4 \cdot - 9}}{2 \cdot 1}$

Multiply $- 4$ by $- 9$ .

$x = \frac{- 12 \pm \sqrt{144 + 36}}{2 \cdot 1}$

Add $144$ and $36$ .

$x = \frac{- 12 \pm \sqrt{180}}{2 \cdot 1}$

Rewrite $180$ as $6^{2} \cdot 5$ .

Factor $36$ out of $180$ .

$x = \frac{- 12 \pm \sqrt{36 (5)}}{2 \cdot 1}$

Rewrite $36$ as $6^{2}$ .

$x = \frac{- 12 \pm \sqrt{6^{2} \cdot 5}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 12 \pm 6 \sqrt{5}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 12 \pm 6 \sqrt{5}}{2}$

Simplify $\frac{- 12 \pm 6 \sqrt{5}}{2}$ .

$x = - 6 \pm 3 \sqrt{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 6 \pm 3 \sqrt{5}$

Decimal Form:

$x = 0.70820393 \dots, - 12.70820393 \dots$