Find the Perfect Square Trinomial x^2+x+1/4

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

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

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

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

One to any power is one.

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

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

$\frac{1}{4}$

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

Combine the numerators over the common denominator.

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

Add $1$ and $1$ .

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

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

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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