Finite Math Examples

$0 = 2 w^{2} + 4 w - 16$

Step 1

Move all the expressions to the left side of the equation.

Tap for more steps...

Step 1.1

Subtract $2 w^{2}$ from both sides of the equation.

$- 2 w^{2} = 4 w - 16$

Step 1.2

Subtract $4 w$ from both sides of the equation.

$- 2 w^{2} - 4 w = - 16$

Step 1.3

Add $16$ to both sides of the equation.

$- 2 w^{2} - 4 w + 16 = 0$

Step 2

Factor $2$ out of $- 2 w^{2} - 4 w + 16$ .

Tap for more steps...

Step 2.1

Factor $2$ out of $- 2 w^{2}$ .

$2 (- w^{2}) - 4 w + 16 = 0$

Step 2.2

Factor $2$ out of $- 4 w$ .

$2 (- w^{2}) + 2 (- 2 w) + 16 = 0$

Step 2.3

Factor $2$ out of $16$ .

$2 (- w^{2}) + 2 (- 2 w) + 2 (8) = 0$

Step 2.4

Factor $2$ out of $2 (- w^{2}) + 2 (- 2 w)$ .

$2 (- w^{2} - 2 w) + 2 (8) = 0$

Step 2.5

Factor $2$ out of $2 (- w^{2} - 2 w) + 2 (8)$ .

$2 (- w^{2} - 2 w + 8) = 0$

Step 3

Factor.

Tap for more steps...

Step 3.1

Factor by grouping.

Tap for more steps...

Step 3.1.1

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = - 1 \cdot 8 = - 8$ and whose sum is $b = - 2$ .

Tap for more steps...

Step 3.1.1.1

Factor $- 2$ out of $- 2 w$ .

$2 (- w^{2} - 2 w + 8) = 0$

Step 3.1.1.2

Rewrite $- 2$ as $2$ plus $- 4$

$2 (- w^{2} + (2 - 4) w + 8) = 0$

Step 3.1.1.3

Apply the distributive property.

$2 (- w^{2} + 2 w - 4 w + 8) = 0$

Step 3.1.2

Factor out the greatest common factor from each group.

Tap for more steps...

Step 3.1.2.1

Group the first two terms and the last two terms.

$2 ((- w^{2} + 2 w) - 4 w + 8) = 0$

Step 3.1.2.2

Factor out the greatest common factor (GCF) from each group.

$2 (w (- w + 2) + 4 (- w + 2)) = 0$

Step 3.1.3

Factor the polynomial by factoring out the greatest common factor, $- w + 2$ .

$2 ((- w + 2) (w + 4)) = 0$

Step 3.2

Remove unnecessary parentheses.

$2 (- w + 2) (w + 4) = 0$

Step 4

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

$- w + 2 = 0$

$w + 4 = 0$

Step 5

Set $- w + 2$ equal to $0$ and solve for $w$ .

Tap for more steps...

Step 5.1

Set $- w + 2$ equal to $0$ .

$- w + 2 = 0$

Step 5.2

Solve $- w + 2 = 0$ for $w$ .

Tap for more steps...

Step 5.2.1

Subtract $2$ from both sides of the equation.

$- w = - 2$

Step 5.2.2

Divide each term in $- w = - 2$ by $- 1$ and simplify.

Tap for more steps...

Step 5.2.2.1

Divide each term in $- w = - 2$ by $- 1$ .

$\frac{- w}{- 1} = \frac{- 2}{- 1}$

Step 5.2.2.2

Simplify the left side.

Tap for more steps...

Step 5.2.2.2.1

Dividing two negative values results in a positive value.

$\frac{w}{1} = \frac{- 2}{- 1}$

Step 5.2.2.2.2

Divide $w$ by $1$ .

$w = \frac{- 2}{- 1}$

Step 5.2.2.3

Simplify the right side.

Tap for more steps...

Step 5.2.2.3.1

Divide $- 2$ by $- 1$ .

$w = 2$

Step 6

Set $w + 4$ equal to $0$ and solve for $w$ .

Tap for more steps...

Step 6.1

Set $w + 4$ equal to $0$ .

$w + 4 = 0$

Step 6.2

Subtract $4$ from both sides of the equation.

$w = - 4$

Step 7

The final solution is all the values that make $2 (- w + 2) (w + 4) = 0$ true.

$w = 2, - 4$