Solve Using the Quadratic Formula 64s^2+48s+9=0

$64 s^{2} + 48 s + 9 = 0$

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 $a = 64$ , $b = 48$ , and $c = 9$ into the quadratic formula and solve for $s$ .

$\frac{- 48 \pm \sqrt{48^{2} - 4 \cdot (64 \cdot 9)}}{2 \cdot 64}$

Step 3

Simplify.

Simplify the numerator.

Raise $48$ to the power of $2$ .

$s = \frac{- 48 \pm \sqrt{2304 - 4 \cdot 64 \cdot 9}}{2 \cdot 64}$

Multiply $- 4 \cdot 64 \cdot 9$ .

Multiply $- 4$ by $64$ .

$s = \frac{- 48 \pm \sqrt{2304 - 256 \cdot 9}}{2 \cdot 64}$

Multiply $- 256$ by $9$ .

$s = \frac{- 48 \pm \sqrt{2304 - 2304}}{2 \cdot 64}$

Subtract $2304$ from $2304$ .

$s = \frac{- 48 \pm \sqrt{0}}{2 \cdot 64}$

Rewrite $0$ as $0^{2}$ .

$s = \frac{- 48 \pm \sqrt{0^{2}}}{2 \cdot 64}$

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

$s = \frac{- 48 \pm 0}{2 \cdot 64}$

$- 48$ plus or minus $0$ is $- 48$ .

$s = \frac{- 48}{2 \cdot 64}$

Multiply $2$ by $64$ .

$s = \frac{- 48}{128}$

Cancel the common factor of $- 48$ and $128$ .

Factor $16$ out of $- 48$ .

$s = \frac{16 (- 3)}{128}$

Cancel the common factors.

Factor $16$ out of $128$ .

$s = \frac{16 \cdot - 3}{16 \cdot 8}$

Cancel the common factor.

$s = \frac{16 \cdot - 3}{16 \cdot 8}$

Rewrite the expression.

$s = \frac{- 3}{8}$

Move the negative in front of the fraction.

$s = - \frac{3}{8}$

Step 4

The final answer is the combination of both solutions.

$s = - \frac{3}{8}$ Double roots