Solve Using the Quadratic Formula 64x^2-25=0

$64 x^{2} - 25 = 0$

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 $c = - 25$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (64 \cdot - 25)}}{2 \cdot 64}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 64 \cdot - 25}}{2 \cdot 64}$

Multiply $- 4 \cdot 64 \cdot - 25$ .

Multiply $- 4$ by $64$ .

$x = \frac{0 \pm \sqrt{0 - 256 \cdot - 25}}{2 \cdot 64}$

Multiply $- 256$ by $- 25$ .

$x = \frac{0 \pm \sqrt{0 + 6400}}{2 \cdot 64}$

Add $0$ and $6400$ .

$x = \frac{0 \pm \sqrt{6400}}{2 \cdot 64}$

Rewrite $6400$ as $80^{2}$ .

$x = \frac{0 \pm \sqrt{80^{2}}}{2 \cdot 64}$

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

$x = \frac{0 \pm 80}{2 \cdot 64}$

Multiply $2$ by $64$ .

$x = \frac{0 \pm 80}{128}$

Simplify $\frac{0 \pm 80}{128}$ .

$x = \frac{\pm 5}{8}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{5}{8}, - \frac{5}{8}$