Find the Perfect Square Trinomial x^2+5/2x

$x^{2} + \frac{5}{2} x$

Step 1

Combine $\frac{5}{2}$ and $x$ .

$x^{2} + \frac{5 x}{2}$

Step 2

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.

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

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

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

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

Multiply $2$ by $2$ .

${(\frac{5}{4})}^{2}$

Apply the product rule to $\frac{5}{4}$ .

$\frac{5^{2}}{4^{2}}$

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

$\frac{25}{4^{2}}$

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

$\frac{25}{16}$

Step 3

Add $\frac{25}{16}$ to get the perfect square trinomial.

$x^{2} + \frac{5}{2} x + \frac{25}{16}$