Solve Using the Quadratic Formula 36x^2-9=0

$36 x^{2} - 9 = 0$

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 $a = 36$ , $b = 0$ , and $c = - 9$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (36 \cdot - 9)}}{2 \cdot 36}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 36 \cdot - 9}}{2 \cdot 36}$

Multiply $- 4 \cdot 36 \cdot - 9$ .

Multiply $- 4$ by $36$ .

$x = \frac{0 \pm \sqrt{0 - 144 \cdot - 9}}{2 \cdot 36}$

Multiply $- 144$ by $- 9$ .

$x = \frac{0 \pm \sqrt{0 + 1296}}{2 \cdot 36}$

Add $0$ and $1296$ .

$x = \frac{0 \pm \sqrt{1296}}{2 \cdot 36}$

Rewrite $1296$ as $36^{2}$ .

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

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

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

Multiply $2$ by $36$ .

$x = \frac{0 \pm 36}{72}$

Simplify $\frac{0 \pm 36}{72}$ .

$x = \frac{\pm 1}{2}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{1}{2}, - \frac{1}{2}$