Find the Perfect Square Trinomial x^2-5/3x+c

$x^{2} - \frac{5}{3} x + c$

Step 1

Simplify each term.

Combine $x$ and $\frac{5}{3}$ .

$x^{2} - \frac{x \cdot 5}{3} + c$

Move $5$ to the left of $x$ .

$x^{2} - \frac{5 x}{3} + c$

Step 2

Move $- \frac{5 x}{3}$ .

$x^{2} + c - \frac{5 x}{3}$

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.

${(- \frac{5}{3} \cdot \frac{1}{2})}^{2}$

Multiply $- \frac{5}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{2}$ by $\frac{5}{3}$ .

${(- \frac{5}{2 \cdot 3})}^{2}$

Multiply $2$ by $3$ .

${(- \frac{5}{6})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $- \frac{5}{6}$ .

${(- 1)}^{2} {(\frac{5}{6})}^{2}$

Apply the product rule to $\frac{5}{6}$ .

${(- 1)}^{2} \frac{5^{2}}{6^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{6^{2}}$

Multiply $\frac{5^{2}}{6^{2}}$ by $1$ .

$\frac{5^{2}}{6^{2}}$

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

$\frac{25}{6^{2}}$

Raise $6$ to the power of $2$ .

$\frac{25}{36}$

Step 4

Simplify each term.

Combine $x$ and $\frac{5}{3}$ .

$x^{2} - \frac{x \cdot 5}{3} + c + \frac{25}{36}$

Move $5$ to the left of $x$ .

$x^{2} - \frac{5 x}{3} + c + \frac{25}{36}$