Find the Perfect Square Trinomial x^2+9/4x

$x^{2} + \frac{9}{4} x$

Step 1

Combine $\frac{9}{4}$ and $x$ .

$x^{2} + \frac{9 x}{4}$

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.

${(\frac{9}{4} \cdot \frac{1}{2})}^{2}$

Multiply $\frac{9}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{9}{4}$ by $\frac{1}{2}$ .

${(\frac{9}{4 \cdot 2})}^{2}$

Multiply $4$ by $2$ .

${(\frac{9}{8})}^{2}$

Apply the product rule to $\frac{9}{8}$ .

$\frac{9^{2}}{8^{2}}$

Raise $9$ to the power of $2$ .

$\frac{81}{8^{2}}$

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

$\frac{81}{64}$

Step 3

Add $\frac{81}{64}$ to get the perfect square trinomial.

$x^{2} + \frac{9}{4} x + \frac{81}{64}$