Algebra Examples

$f (6) = x^{2} + 3 x - \frac{x}{2}$

Step 1

Replace the variable $x$ with $6$ in the expression.

$f (6) = {(6)}^{2} + 3 (6) - \frac{6}{2}$

Step 2

Simplify the result.

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Step 2.1

Find the common denominator.

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Step 2.1.1

Write ${(6)}^{2}$ as a fraction with denominator $1$ .

$f (6) = \frac{{(6)}^{2}}{1} + 3 (6) - \frac{6}{2}$

Step 2.1.2

Multiply $\frac{{(6)}^{2}}{1}$ by $\frac{2}{2}$ .

$f (6) = \frac{{(6)}^{2}}{1} \cdot \frac{2}{2} + 3 (6) - \frac{6}{2}$

Step 2.1.3

Multiply $\frac{{(6)}^{2}}{1}$ by $\frac{2}{2}$ .

$f (6) = \frac{{(6)}^{2} \cdot 2}{2} + 3 (6) - \frac{6}{2}$

Step 2.1.4

Write $3 (6)$ as a fraction with denominator $1$ .

$f (6) = \frac{{(6)}^{2} \cdot 2}{2} + \frac{3 (6)}{1} - \frac{6}{2}$

Step 2.1.5

Multiply $\frac{3 (6)}{1}$ by $\frac{2}{2}$ .

$f (6) = \frac{{(6)}^{2} \cdot 2}{2} + \frac{3 (6)}{1} \cdot \frac{2}{2} - \frac{6}{2}$

Step 2.1.6

Multiply $\frac{3 (6)}{1}$ by $\frac{2}{2}$ .

$f (6) = \frac{{(6)}^{2} \cdot 2}{2} + \frac{3 (6) \cdot 2}{2} - \frac{6}{2}$

Step 2.2

Combine the numerators over the common denominator.

$f (6) = \frac{{(6)}^{2} \cdot 2 + 3 (6) \cdot 2 - 6}{2}$

Step 2.3

Simplify each term.

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Step 2.3.1

Raise $6$ to the power of $2$ .

$f (6) = \frac{36 \cdot 2 + 3 (6) \cdot 2 - 6}{2}$

Step 2.3.2

Multiply $36$ by $2$ .

$f (6) = \frac{72 + 3 (6) \cdot 2 - 6}{2}$

Step 2.3.3

Multiply $3 (6) \cdot 2$ .

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Step 2.3.3.1

Multiply $3$ by $6$ .

$f (6) = \frac{72 + 18 \cdot 2 - 6}{2}$

Step 2.3.3.2

Multiply $18$ by $2$ .

$f (6) = \frac{72 + 36 - 6}{2}$

Step 2.4

Simplify the expression.

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Step 2.4.1

Add $72$ and $36$ .

$f (6) = \frac{108 - 6}{2}$

Step 2.4.2

Subtract $6$ from $108$ .

$f (6) = \frac{102}{2}$

Step 2.4.3

Divide $102$ by $2$ .

$f (6) = 51$

Step 2.5

The final answer is $51$ .

$51$

Step 3