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

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

Combine $\frac{1}{4}$ and $x$ .

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

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

Multiply the numerator by the reciprocal of the denominator.

${(\frac{1}{4} \cdot \frac{1}{2})}^{2}$

Multiply $\frac{1}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{4}$ by $\frac{1}{2}$ .

${(\frac{1}{4 \cdot 2})}^{2}$

Multiply $4$ by $2$ .

${(\frac{1}{8})}^{2}$

Apply the product rule to $\frac{1}{8}$ .

$\frac{1^{2}}{8^{2}}$

One to any power is one.

$\frac{1}{8^{2}}$

Raise $8$ to the power of $2$ .

$\frac{1}{64}$

Add $\frac{1}{64}$ to get the perfect square trinomial.

$x^{2} + \frac{1}{4} x + \frac{1}{64}$