Algebra Examples

$x^{2} + x + \frac{1}{4}$

Step 1

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 1.1

Apply the product rule to $\frac{1}{2}$ .

$\frac{1^{2}}{2^{2}}$

Step 1.2

One to any power is one.

$\frac{1}{2^{2}}$

Step 1.3

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

$\frac{1}{4}$

Step 2

Add $\frac{1}{4}$ to get the perfect square trinomial.

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Step 2.1

Combine the numerators over the common denominator.

$x^{2} + x + \frac{1 + 1}{4}$

Step 2.2

Add $1$ and $1$ .

$x^{2} + x + \frac{2}{4}$

Step 2.3

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

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Step 2.3.1

Factor $2$ out of $2$ .

$x^{2} + x + \frac{2 (1)}{4}$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Factor $2$ out of $4$ .

$x^{2} + x + \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.3.2.2

Cancel the common factor.

$x^{2} + x + \frac{2 \cdot 1}{2 \cdot 2}$

Step 2.3.2.3

Rewrite the expression.

$x^{2} + x + \frac{1}{2}$