Solve Using the Quadratic Formula 2x^2-6=0

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

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 $a = 2$ , $b = 0$ , and $c = - 6$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot - 6)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot - 6}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 6$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot - 6}}{2 \cdot 2}$

Multiply $- 8$ by $- 6$ .

$x = \frac{0 \pm \sqrt{0 + 48}}{2 \cdot 2}$

Add $0$ and $48$ .

$x = \frac{0 \pm \sqrt{48}}{2 \cdot 2}$

Rewrite $48$ as $4^{2} \cdot 3$ .

Factor $16$ out of $48$ .

$x = \frac{0 \pm \sqrt{16 (3)}}{2 \cdot 2}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{0 \pm \sqrt{4^{2} \cdot 3}}{2 \cdot 2}$

Pull terms out from under the radical.

$x = \frac{0 \pm 4 \sqrt{3}}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{0 \pm 4 \sqrt{3}}{4}$

Simplify $\frac{0 \pm 4 \sqrt{3}}{4}$ .

$x = \pm \sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{3}$

Decimal Form:

$x = 1.73205080 \dots, - 1.73205080 \dots$