Calculus Examples

$4 w^{2} + 20 w + 25 = 0$

Step 1

Factor using the perfect square rule.

Tap for more steps...

Step 1.1

Rewrite $4 w^{2}$ as ${(2 w)}^{2}$ .

${(2 w)}^{2} + 20 w + 25 = 0$

Step 1.2

Rewrite $25$ as $5^{2}$ .

${(2 w)}^{2} + 20 w + 5^{2} = 0$

Step 1.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$20 w = 2 \cdot (2 w) \cdot 5$

Step 1.4

Rewrite the polynomial.

${(2 w)}^{2} + 2 \cdot (2 w) \cdot 5 + 5^{2} = 0$

Step 1.5

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = 2 w$ and $b = 5$ .

${(2 w + 5)}^{2} = 0$

Step 2

Set the $2 w + 5$ equal to $0$ .

$2 w + 5 = 0$

Step 3

Solve for $w$ .

Tap for more steps...

Step 3.1

Subtract $5$ from both sides of the equation.

$2 w = - 5$

Step 3.2

Divide each term in $2 w = - 5$ by $2$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $2 w = - 5$ by $2$ .

$\frac{2 w}{2} = \frac{- 5}{2}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{2 w}{2} = \frac{- 5}{2}$

Step 3.2.2.1.2

Divide $w$ by $1$ .

$w = \frac{- 5}{2}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Move the negative in front of the fraction.

$w = - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$w = - \frac{5}{2}$

Decimal Form:

$w = - 2.5$

Mixed Number Form:

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