Solve Using the Quadratic Formula 9x^2-21=0

$9 x^{2} - 21 = 0$

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 $a = 9$ , $b = 0$ , and $c = - 21$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (9 \cdot - 21)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 9 \cdot - 21}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 21$ .

Multiply $- 4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 36 \cdot - 21}}{2 \cdot 9}$

Multiply $- 36$ by $- 21$ .

$x = \frac{0 \pm \sqrt{0 + 756}}{2 \cdot 9}$

Add $0$ and $756$ .

$x = \frac{0 \pm \sqrt{756}}{2 \cdot 9}$

Rewrite $756$ as $6^{2} \cdot 21$ .

Factor $36$ out of $756$ .

$x = \frac{0 \pm \sqrt{36 (21)}}{2 \cdot 9}$

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

$x = \frac{0 \pm \sqrt{6^{2} \cdot 21}}{2 \cdot 9}$

Pull terms out from under the radical.

$x = \frac{0 \pm 6 \sqrt{21}}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{0 \pm 6 \sqrt{21}}{18}$

Simplify $\frac{0 \pm 6 \sqrt{21}}{18}$ .

$x = \frac{\pm \sqrt{21}}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\pm \sqrt{21}}{3}$

Decimal Form:

$x = 1.52752523 \dots, - 1.52752523 \dots$