Find the Perfect Square Trinomial s^2+3/4s+9/64

$s^{2} + \frac{3}{4} s + \frac{9}{64}$

Step 1

Combine $\frac{3}{4}$ and $s$ .

$s^{2} + \frac{3 s}{4} + \frac{9}{64}$

Step 2

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

Multiply the numerator by the reciprocal of the denominator.

${(\frac{3}{4} \cdot \frac{1}{2})}^{2}$

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

${(\frac{3}{4 \cdot 2})}^{2}$

Multiply $4$ by $2$ .

${(\frac{3}{8})}^{2}$

Apply the product rule to $\frac{3}{8}$ .

$\frac{3^{2}}{8^{2}}$

Raise $3$ to the power of $2$ .

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

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

$\frac{9}{64}$

Step 3

Add $\frac{9}{64}$ to get the perfect square trinomial.

Combine fractions.

Combine the numerators over the common denominator.

$s^{2} + \frac{3}{4} s + \frac{9 + 9}{64}$

Add $9$ and $9$ .

$s^{2} + \frac{3}{4} s + \frac{18}{64}$

Simplify each term.

Combine $\frac{3}{4}$ and $s$ .

$s^{2} + \frac{3 s}{4} + \frac{18}{64}$

Cancel the common factor of $18$ and $64$ .

Factor $2$ out of $18$ .

$s^{2} + \frac{3 s}{4} + \frac{2 (9)}{64}$

Cancel the common factors.

Factor $2$ out of $64$ .

$s^{2} + \frac{3 s}{4} + \frac{2 \cdot 9}{2 \cdot 32}$

Cancel the common factor.

$s^{2} + \frac{3 s}{4} + \frac{2 \cdot 9}{2 \cdot 32}$

Rewrite the expression.

$s^{2} + \frac{3 s}{4} + \frac{9}{32}$