Finite Math Examples

$v^{2} - 6 v - 14 = 2$

Step 1

Subtract $2$ from both sides of the equation.

$v^{2} - 6 v - 14 - 2 = 0$

Step 2

Subtract $2$ from $- 14$ .

$v^{2} - 6 v - 16 = 0$

Step 3

Factor $v^{2} - 6 v - 16$ using the AC method.

Tap for more steps...

Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 16$ and whose sum is $- 6$ .

$- 8, 2$

Step 3.2

Write the factored form using these integers.

$(v - 8) (v + 2) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$v - 8 = 0$

$v + 2 = 0$

Step 5

Set $v - 8$ equal to $0$ and solve for $v$ .

Tap for more steps...

Step 5.1

Set $v - 8$ equal to $0$ .

$v - 8 = 0$

Step 5.2

Add $8$ to both sides of the equation.

$v = 8$

Step 6

Set $v + 2$ equal to $0$ and solve for $v$ .

Tap for more steps...

Step 6.1

Set $v + 2$ equal to $0$ .

$v + 2 = 0$

Step 6.2

Subtract $2$ from both sides of the equation.

$v = - 2$

Step 7

The final solution is all the values that make $(v - 8) (v + 2) = 0$ true.

$v = 8, - 2$