Solve Using the Quadratic Formula 32=25x^2-4

$32 = 25 x^{2} - 4$

Step 1

Move all terms to the left side of the equation and simplify.

Move all the expressions to the left side of the equation.

Subtract $25 x^{2}$ from both sides of the equation.

$32 - 25 x^{2} = - 4$

Add $4$ to both sides of the equation.

$32 - 25 x^{2} + 4 = 0$

Add $32$ and $4$ .

$- 25 x^{2} + 36 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = - 25$ , $b = 0$ , and $c = 36$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (- 25 \cdot 36)}}{2 \cdot - 25}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 25 \cdot 36}}{2 \cdot - 25}$

Multiply $- 4 \cdot - 25 \cdot 36$ .

Multiply $- 4$ by $- 25$ .

$x = \frac{0 \pm \sqrt{0 + 100 \cdot 36}}{2 \cdot - 25}$

Multiply $100$ by $36$ .

$x = \frac{0 \pm \sqrt{0 + 3600}}{2 \cdot - 25}$

Add $0$ and $3600$ .

$x = \frac{0 \pm \sqrt{3600}}{2 \cdot - 25}$

Rewrite $3600$ as $60^{2}$ .

$x = \frac{0 \pm \sqrt{60^{2}}}{2 \cdot - 25}$

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

$x = \frac{0 \pm 60}{2 \cdot - 25}$

Multiply $2$ by $- 25$ .

$x = \frac{0 \pm 60}{- 50}$

Simplify $\frac{0 \pm 60}{- 50}$ .

$x = \frac{\pm 6}{5}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{6}{5}, - \frac{6}{5}$