Algebra Examples

$f (10) = \frac{1}{2} x^{2} + 2 x - 5$

Step 1

Divide each term in $f (10) = \frac{1}{2} x^{2} + 2 x - 5$ by $10$ .

$\frac{f \cdot 10}{10} = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $10$ .

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Step 2.1.1

Cancel the common factor.

$\frac{f \cdot 10}{10} = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 2.1.2

Divide $f$ by $1$ .

$f = \frac{\frac{1}{2} x^{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3

Simplify the right side.

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Step 3.1

Simplify each term.

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Step 3.1.1

Combine $\frac{1}{2}$ and $x^{2}$ .

$f = \frac{\frac{x^{2}}{2}}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3.1.2

Multiply the numerator by the reciprocal of the denominator.

$f = \frac{x^{2}}{2} \cdot \frac{1}{10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3.1.3

Combine.

$f = \frac{x^{2} \cdot 1}{2 \cdot 10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3.1.4

Multiply $x^{2}$ by $1$ .

$f = \frac{x^{2}}{2 \cdot 10} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3.1.5

Multiply $2$ by $10$ .

$f = \frac{x^{2}}{20} + \frac{2 x}{10} + \frac{- 5}{10}$

Step 3.1.6

Cancel the common factor of $2$ and $10$ .

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Step 3.1.6.1

Factor $2$ out of $2 x$ .

$f = \frac{x^{2}}{20} + \frac{2 (x)}{10} + \frac{- 5}{10}$

Step 3.1.6.2

Cancel the common factors.

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Step 3.1.6.2.1

Factor $2$ out of $10$ .

$f = \frac{x^{2}}{20} + \frac{2 x}{2 \cdot 5} + \frac{- 5}{10}$

Step 3.1.6.2.2

Cancel the common factor.

$f = \frac{x^{2}}{20} + \frac{2 x}{2 \cdot 5} + \frac{- 5}{10}$

Step 3.1.6.2.3

Rewrite the expression.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{- 5}{10}$

Step 3.1.7

Cancel the common factor of $- 5$ and $10$ .

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Step 3.1.7.1

Factor $5$ out of $- 5$ .

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 (- 1)}{10}$

Step 3.1.7.2

Cancel the common factors.

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Step 3.1.7.2.1

Factor $5$ out of $10$ .

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Step 3.1.7.2.2

Cancel the common factor.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{5 \cdot - 1}{5 \cdot 2}$

Step 3.1.7.2.3

Rewrite the expression.

$f = \frac{x^{2}}{20} + \frac{x}{5} + \frac{- 1}{2}$

Step 3.1.8

Move the negative in front of the fraction.

$f = \frac{x^{2}}{20} + \frac{x}{5} - \frac{1}{2}$