Trigonometry Examples

$s = 2 w^{2} + 4 w h$

Step 1

Rewrite the equation as $2 w^{2} + 4 w h = s$ .

$2 w^{2} + 4 w h = s$

Step 2

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

$4 w h = s - 2 w^{2}$

Step 3

Divide each term in $4 w h = s - 2 w^{2}$ by $4 w$ and simplify.

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Step 3.1

Divide each term in $4 w h = s - 2 w^{2}$ by $4 w$ .

$\frac{4 w h}{4 w} = \frac{s}{4 w} + \frac{- 2 w^{2}}{4 w}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $4$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{4 w h}{4 w} = \frac{s}{4 w} + \frac{- 2 w^{2}}{4 w}$

Step 3.2.1.2

Rewrite the expression.

$\frac{w h}{w} = \frac{s}{4 w} + \frac{- 2 w^{2}}{4 w}$

Step 3.2.2

Cancel the common factor of $w$ .

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Step 3.2.2.1

Cancel the common factor.

$\frac{w h}{w} = \frac{s}{4 w} + \frac{- 2 w^{2}}{4 w}$

Step 3.2.2.2

Divide $h$ by $1$ .

$h = \frac{s}{4 w} + \frac{- 2 w^{2}}{4 w}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $- 2$ and $4$ .

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Step 3.3.1.1.1

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

$h = \frac{s}{4 w} + \frac{2 (- w^{2})}{4 w}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $2$ out of $4 w$ .

$h = \frac{s}{4 w} + \frac{2 (- w^{2})}{2 (2 w)}$

Step 3.3.1.1.2.2

Cancel the common factor.

$h = \frac{s}{4 w} + \frac{2 (- w^{2})}{2 (2 w)}$

Step 3.3.1.1.2.3

Rewrite the expression.

$h = \frac{s}{4 w} + \frac{- w^{2}}{2 w}$

Step 3.3.1.2

Cancel the common factor of $w^{2}$ and $w$ .

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Step 3.3.1.2.1

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

$h = \frac{s}{4 w} + \frac{w (- w)}{2 w}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $w$ out of $2 w$ .

$h = \frac{s}{4 w} + \frac{w (- w)}{w \cdot 2}$

Step 3.3.1.2.2.2

Cancel the common factor.

$h = \frac{s}{4 w} + \frac{w (- w)}{w \cdot 2}$

Step 3.3.1.2.2.3

Rewrite the expression.

$h = \frac{s}{4 w} + \frac{- w}{2}$

Step 3.3.1.3

Move the negative in front of the fraction.

$h = \frac{s}{4 w} - \frac{w}{2}$