Solve Using the Quadratic Formula 9x^2-81=0

$9 x^{2} - 81 = 0$

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 $c = - 81$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (9 \cdot - 81)}}{2 \cdot 9}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 9 \cdot - 81}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 81$ .

Multiply $- 4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 36 \cdot - 81}}{2 \cdot 9}$

Multiply $- 36$ by $- 81$ .

$x = \frac{0 \pm \sqrt{0 + 2916}}{2 \cdot 9}$

Add $0$ and $2916$ .

$x = \frac{0 \pm \sqrt{2916}}{2 \cdot 9}$

Rewrite $2916$ as $54^{2}$ .

$x = \frac{0 \pm \sqrt{54^{2}}}{2 \cdot 9}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{0 \pm 54}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{0 \pm 54}{18}$

Simplify $\frac{0 \pm 54}{18}$ .

$x = \pm 3$

Step 4

The final answer is the combination of both solutions.

$x = 3, - 3$