Solve Using the Quadratic Formula 64x^2-1=0

$64 x^{2} - 1 = 0$

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 $a = 64$ , $b = 0$ , and $c = - 1$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (64 \cdot - 1)}}{2 \cdot 64}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 64 \cdot - 1}}{2 \cdot 64}$

Multiply $- 4 \cdot 64 \cdot - 1$ .

Multiply $- 4$ by $64$ .

$x = \frac{0 \pm \sqrt{0 - 256 \cdot - 1}}{2 \cdot 64}$

Multiply $- 256$ by $- 1$ .

$x = \frac{0 \pm \sqrt{0 + 256}}{2 \cdot 64}$

Add $0$ and $256$ .

$x = \frac{0 \pm \sqrt{256}}{2 \cdot 64}$

Rewrite $256$ as $16^{2}$ .

$x = \frac{0 \pm \sqrt{16^{2}}}{2 \cdot 64}$

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

$x = \frac{0 \pm 16}{2 \cdot 64}$

Multiply $2$ by $64$ .

$x = \frac{0 \pm 16}{128}$

Simplify $\frac{0 \pm 16}{128}$ .

$x = \frac{\pm 1}{8}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{1}{8}, - \frac{1}{8}$