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

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

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 $a = 2$ , $b = 0$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (2 \cdot - 9)}}{2 \cdot 2}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 2 \cdot - 9}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 9$ .

Multiply $- 4$ by $2$ .

$x = \frac{0 \pm \sqrt{0 - 8 \cdot - 9}}{2 \cdot 2}$

Multiply $- 8$ by $- 9$ .

$x = \frac{0 \pm \sqrt{0 + 72}}{2 \cdot 2}$

Add $0$ and $72$ .

$x = \frac{0 \pm \sqrt{72}}{2 \cdot 2}$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$x = \frac{0 \pm \sqrt{36 (2)}}{2 \cdot 2}$

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

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

Pull terms out from under the radical.

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

Multiply $2$ by $2$ .

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

Simplify $\frac{0 \pm 6 \sqrt{2}}{4}$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = 2.12132034 \dots, - 2.12132034 \dots$