Finite Math Examples

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

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

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

Step 3

Simplify.

Tap for more steps...

Step 3.1

Simplify the numerator.

Tap for more steps...

Step 3.1.1

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

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

Step 3.1.2

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

Tap for more steps...

Step 3.1.2.1

Multiply $- 4$ by $9$ .

$s = \frac{- 48 \pm \sqrt{2304 - 36 \cdot 64}}{2 \cdot 9}$

Step 3.1.2.2

Multiply $- 36$ by $64$ .

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

Step 3.1.3

Subtract $2304$ from $2304$ .

$s = \frac{- 48 \pm \sqrt{0}}{2 \cdot 9}$

Step 3.1.4

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

$s = \frac{- 48 \pm \sqrt{0^{2}}}{2 \cdot 9}$

Step 3.1.5

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

$s = \frac{- 48 \pm 0}{2 \cdot 9}$

Step 3.1.6

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

$s = \frac{- 48}{2 \cdot 9}$

Step 3.2

Multiply $2$ by $9$ .

$s = \frac{- 48}{18}$

Step 3.3

Cancel the common factor of $- 48$ and $18$ .

Tap for more steps...

Step 3.3.1

Factor $6$ out of $- 48$ .

$s = \frac{6 (- 8)}{18}$

Step 3.3.2

Cancel the common factors.

Tap for more steps...

Step 3.3.2.1

Factor $6$ out of $18$ .

$s = \frac{6 \cdot - 8}{6 \cdot 3}$

Step 3.3.2.2

Cancel the common factor.

$s = \frac{6 \cdot - 8}{6 \cdot 3}$

Step 3.3.2.3

Rewrite the expression.

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

Step 3.4

Move the negative in front of the fraction.

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

Step 4

The final answer is the combination of both solutions.

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