Finite Math Examples

$(r - 2) (r + 16) = - 6$

Step 1

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

Tap for more steps...

Step 1.1

Simplify the left side.

Tap for more steps...

Step 1.1.1

Simplify $(r - 2) (r + 16)$ .

Tap for more steps...

Step 1.1.1.1

Expand $(r - 2) (r + 16)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1.1.1

Apply the distributive property.

$r (r + 16) - 2 (r + 16) = - 6$

Step 1.1.1.1.2

Apply the distributive property.

$r \cdot r + r \cdot 16 - 2 (r + 16) = - 6$

Step 1.1.1.1.3

Apply the distributive property.

$r \cdot r + r \cdot 16 - 2 r - 2 \cdot 16 = - 6$

Step 1.1.1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.1.1.2.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.1.1

Multiply $r$ by $r$ .

$r^{2} + r \cdot 16 - 2 r - 2 \cdot 16 = - 6$

Step 1.1.1.2.1.2

Move $16$ to the left of $r$ .

$r^{2} + 16 \cdot r - 2 r - 2 \cdot 16 = - 6$

Step 1.1.1.2.1.3

Multiply $- 2$ by $16$ .

$r^{2} + 16 r - 2 r - 32 = - 6$

Step 1.1.1.2.2

Subtract $2 r$ from $16 r$ .

$r^{2} + 14 r - 32 = - 6$

Step 1.2

Add $6$ to both sides of the equation.

$r^{2} + 14 r - 32 + 6 = 0$

Step 1.3

Add $- 32$ and $6$ .

$r^{2} + 14 r - 26 = 0$

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 $a = 1$ , $b = 14$ , and $c = - 26$ into the quadratic formula and solve for $r$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (1 \cdot - 26)}}{2 \cdot 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Raise $14$ to the power of $2$ .

$r = \frac{- 14 \pm \sqrt{196 - 4 \cdot 1 \cdot - 26}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 26$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $1$ .

$r = \frac{- 14 \pm \sqrt{196 - 4 \cdot - 26}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 26$ .

$r = \frac{- 14 \pm \sqrt{196 + 104}}{2 \cdot 1}$

Step 4.1.3

Add $196$ and $104$ .

$r = \frac{- 14 \pm \sqrt{300}}{2 \cdot 1}$

Step 4.1.4

Rewrite $300$ as $10^{2} \cdot 3$ .

Tap for more steps...

Step 4.1.4.1

Factor $100$ out of $300$ .

$r = \frac{- 14 \pm \sqrt{100 (3)}}{2 \cdot 1}$

Step 4.1.4.2

Rewrite $100$ as $10^{2}$ .

$r = \frac{- 14 \pm \sqrt{10^{2} \cdot 3}}{2 \cdot 1}$

Step 4.1.5

Pull terms out from under the radical.

$r = \frac{- 14 \pm 10 \sqrt{3}}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$r = \frac{- 14 \pm 10 \sqrt{3}}{2}$

Step 4.3

Simplify $\frac{- 14 \pm 10 \sqrt{3}}{2}$ .

$r = - 7 \pm 5 \sqrt{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$r = - 7 \pm 5 \sqrt{3}$

Decimal Form:

$r = 1.66025403 \dots, - 15.66025403 \dots$