Algebra Examples

$x^{2} + \frac{5}{6} x + \frac{25}{144}$

Step 1

Combine $\frac{5}{6}$ and $x$ .

$x^{2} + \frac{5 x}{6} + \frac{25}{144}$

Step 2

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

${(\frac{5}{6} \cdot \frac{1}{2})}^{2}$

Step 2.2

Multiply $\frac{5}{6} \cdot \frac{1}{2}$ .

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Step 2.2.1

Multiply $\frac{5}{6}$ by $\frac{1}{2}$ .

${(\frac{5}{6 \cdot 2})}^{2}$

Step 2.2.2

Multiply $6$ by $2$ .

${(\frac{5}{12})}^{2}$

Step 2.3

Apply the product rule to $\frac{5}{12}$ .

$\frac{5^{2}}{12^{2}}$

Step 2.4

Raise $5$ to the power of $2$ .

$\frac{25}{12^{2}}$

Step 2.5

Raise $12$ to the power of $2$ .

$\frac{25}{144}$

Step 3

Add $\frac{25}{144}$ to get the perfect square trinomial.

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Step 3.1

Combine fractions.

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Step 3.1.1

Combine the numerators over the common denominator.

$x^{2} + \frac{5}{6} x + \frac{25 + 25}{144}$

Step 3.1.2

Add $25$ and $25$ .

$x^{2} + \frac{5}{6} x + \frac{50}{144}$

Step 3.2

Simplify each term.

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Step 3.2.1

Combine $\frac{5}{6}$ and $x$ .

$x^{2} + \frac{5 x}{6} + \frac{50}{144}$

Step 3.2.2

Cancel the common factor of $50$ and $144$ .

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Step 3.2.2.1

Factor $2$ out of $50$ .

$x^{2} + \frac{5 x}{6} + \frac{2 (25)}{144}$

Step 3.2.2.2

Cancel the common factors.

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Step 3.2.2.2.1

Factor $2$ out of $144$ .

$x^{2} + \frac{5 x}{6} + \frac{2 \cdot 25}{2 \cdot 72}$

Step 3.2.2.2.2

Cancel the common factor.

$x^{2} + \frac{5 x}{6} + \frac{2 \cdot 25}{2 \cdot 72}$

Step 3.2.2.2.3

Rewrite the expression.

$x^{2} + \frac{5 x}{6} + \frac{25}{72}$