Solve for x x^2+6x-6=0

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

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

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

Step 3

Simplify.

Simplify the numerator.

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

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

Multiply $- 4 \cdot 1 \cdot - 6$ .

Multiply $- 4$ by $1$ .

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

Multiply $- 4$ by $- 6$ .

$x = \frac{- 6 \pm \sqrt{36 + 24}}{2 \cdot 1}$

Add $36$ and $24$ .

$x = \frac{- 6 \pm \sqrt{60}}{2 \cdot 1}$

Rewrite $60$ as $2^{2} \cdot 15$ .

Factor $4$ out of $60$ .

$x = \frac{- 6 \pm \sqrt{4 (15)}}{2 \cdot 1}$

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

$x = \frac{- 6 \pm \sqrt{2^{2} \cdot 15}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{- 6 \pm 2 \sqrt{15}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{- 6 \pm 2 \sqrt{15}}{2}$

Simplify $\frac{- 6 \pm 2 \sqrt{15}}{2}$ .

$x = - 3 \pm \sqrt{15}$

Step 4

The final answer is the combination of both solutions.

$x = - 3 + \sqrt{15}, - 3 - \sqrt{15}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 3 + \sqrt{15}, - 3 - \sqrt{15}$

Decimal Form:

$x = 0.87298334 \dots, - 6.87298334 \dots$