Solve Using the Quadratic Formula 25x^2-16=0

$25 x^{2} - 16 = 0$

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 $a = 25$ , $b = 0$ , and $c = - 16$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (25 \cdot - 16)}}{2 \cdot 25}$

Step 3

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 25 \cdot - 16}}{2 \cdot 25}$

Multiply $- 4 \cdot 25 \cdot - 16$ .

Multiply $- 4$ by $25$ .

$x = \frac{0 \pm \sqrt{0 - 100 \cdot - 16}}{2 \cdot 25}$

Multiply $- 100$ by $- 16$ .

$x = \frac{0 \pm \sqrt{0 + 1600}}{2 \cdot 25}$

Add $0$ and $1600$ .

$x = \frac{0 \pm \sqrt{1600}}{2 \cdot 25}$

Rewrite $1600$ as $40^{2}$ .

$x = \frac{0 \pm \sqrt{40^{2}}}{2 \cdot 25}$

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

$x = \frac{0 \pm 40}{2 \cdot 25}$

Multiply $2$ by $25$ .

$x = \frac{0 \pm 40}{50}$

Simplify $\frac{0 \pm 40}{50}$ .

$x = \frac{\pm 4}{5}$

Step 4

The final answer is the combination of both solutions.

$x = \frac{4}{5}, - \frac{4}{5}$