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

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

Step 1

Combine $\frac{1}{2}$ and $x$ .

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

Step 2

Move $\frac{x}{2}$ .

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

Step 3

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.

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

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

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

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

Multiply $2$ by $2$ .

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

Apply the product rule to $\frac{1}{4}$ .

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

One to any power is one.

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

Raise $4$ to the power of $2$ .

$\frac{1}{16}$

Step 4

Combine $\frac{1}{2}$ and $x$ .

$x^{2} + \frac{x}{2} + c + \frac{1}{16}$