Solve Using the Quadratic Formula 9x^2=25

$9 x^{2} = 25$

Step 1

Subtract $25$ from both sides of the equation.

$9 x^{2} - 25 = 0$

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 $a = 9$ , $b = 0$ , and $c = - 25$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (9 \cdot - 25)}}{2 \cdot 9}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 9 \cdot - 25}}{2 \cdot 9}$

Multiply $- 4 \cdot 9 \cdot - 25$ .

Multiply $- 4$ by $9$ .

$x = \frac{0 \pm \sqrt{0 - 36 \cdot - 25}}{2 \cdot 9}$

Multiply $- 36$ by $- 25$ .

$x = \frac{0 \pm \sqrt{0 + 900}}{2 \cdot 9}$

Add $0$ and $900$ .

$x = \frac{0 \pm \sqrt{900}}{2 \cdot 9}$

Rewrite $900$ as $30^{2}$ .

$x = \frac{0 \pm \sqrt{30^{2}}}{2 \cdot 9}$

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

$x = \frac{0 \pm 30}{2 \cdot 9}$

Multiply $2$ by $9$ .

$x = \frac{0 \pm 30}{18}$

Simplify $\frac{0 \pm 30}{18}$ .

$x = \frac{\pm 5}{3}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{3}, - \frac{5}{3}$