Calculus Examples

$36 x - \frac{9}{2} x^{2} = 0$

Step 1

Simplify each term.

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Step 1.1

Combine $x^{2}$ and $\frac{9}{2}$ .

$36 x - \frac{x^{2} \cdot 9}{2} = 0$

Step 1.2

Move $9$ to the left of $x^{2}$ .

$36 x - \frac{9 x^{2}}{2} = 0$

Step 2

Factor $9 x$ out of $36 x - \frac{9 x^{2}}{2}$ .

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Step 2.1

Factor $9 x$ out of $36 x$ .

$9 x (4) - \frac{9 x^{2}}{2} = 0$

Step 2.2

Factor $9 x$ out of $- \frac{9 x^{2}}{2}$ .

$9 x (4) + 9 x (- \frac{x}{2}) = 0$

Step 2.3

Factor $9 x$ out of $9 x (4) + 9 x (- \frac{x}{2})$ .

$9 x (4 - \frac{x}{2}) = 0$

Step 3

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

$x = 0$

$4 - \frac{x}{2} = 0$

Step 4

Set $x$ equal to $0$ .

$x = 0$

Step 5

Set $4 - \frac{x}{2}$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $4 - \frac{x}{2}$ equal to $0$ .

$4 - \frac{x}{2} = 0$

Step 5.2

Solve $4 - \frac{x}{2} = 0$ for $x$ .

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Step 5.2.1

Subtract $4$ from both sides of the equation.

$- \frac{x}{2} = - 4$

Step 5.2.2

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot - 4$

Step 5.2.3

Simplify both sides of the equation.

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Step 5.2.3.1

Simplify the left side.

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Step 5.2.3.1.1

Simplify $- 2 (- \frac{x}{2})$ .

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Step 5.2.3.1.1.1

Cancel the common factor of $2$ .

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Step 5.2.3.1.1.1.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 \cdot - 4$

Step 5.2.3.1.1.1.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot - 4$

Step 5.2.3.1.1.1.3

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 \cdot - 4$

Step 5.2.3.1.1.1.4

Rewrite the expression.

$- - x = - 2 \cdot - 4$

Step 5.2.3.1.1.2

Multiply.

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Step 5.2.3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot - 4$

Step 5.2.3.1.1.2.2

Multiply $x$ by $1$ .

$x = - 2 \cdot - 4$

Step 5.2.3.2

Simplify the right side.

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Step 5.2.3.2.1

Multiply $- 2$ by $- 4$ .

$x = 8$

Step 6

The final solution is all the values that make $9 x (4 - \frac{x}{2}) = 0$ true.

$x = 0, 8$